I am going to assume that "major symbol" refers to a reoccurring symbol in Home Fire, of which the only one I can think of immediately would be hot/cold, which encompasses snow and the seasons.
As a bit of thinking out loud, I feel that at a first glance, the symbolism of the temperature is somewhat inconsistent. In Isma's section, there are several mentions of snow; as a class, we hypothesized that the snow symbolized a variety of things, namely forced assimilation, ostracization, and general inhospitality. Despite this, Karamat Lone, who parallels Isma, prefers warmth over the cold. This may be explained by saying that Karamat as an individual rather than a politician desires acceptance and the like, but he says that "a man needed fire in his veins to burn through the world, not ice to freeze everything in place." (Shamsie 227) The immediate correlation of the symbolism of heat versus cold would be progress versus stagnation, but it would be odd to use this lens when considering Isma's section.
To explain why Isma and Karamat having differing views on the temperature is somewhat boggling symbolically, we have to do minor character studies of the two. Isma, at least outwardly, accepts conformity, and her religious beliefs, although strong, shows incredible distaste for extremist Muslims, stemming from her hatred of her father. When she steps into the US and is met with snow, it could indicate her need to conform to beliefs that she doesn't necessarily hold, or it could indicate her isolation from those she cherishes.
Karamat Lone is Isma's character pushed to an extreme. Although Karamat is not Islamophobic, he takes a firm stance concerning the behavior of Muslims in general, and detests extremists who are "Muslims who make people hate Muslims." (Shamsie 244) He doesn't simply accept conformity as a positive good, he is the one spearheading conformity and rallying the public to force conformity. As a whole Karamat spends his character arc desiring warmth and fire rather than having it. His hands are cold when drinking coffee, a sensation he finds mildly displeasing; drinking the coffee and having the heat sear his throat is desirable. When he is barred from the warmth of his bedroom, Karamat makes his way out to the veranda, where the night wind laps against his cheeks, cold. In these contexts, it would be reasonable to assume that warmth is human connection, and cold is isolation. Unfortunately, temperature is brought up in situations beyond that of simple emotion.
When speaking to Isma about her family, Karamat says that should an angel bring Aneeka and Parvaiz back on "wings of fire," he would still keep them from entering Britain. Could the angel's wings symbolize bringing Isma's family back to her, where she was previously cold and isolated? An argument could be made, but the emphasis placed upon the phrasing and the strength of the statement makes such an interpretation feel somewhat lacking. Also, going back to the quote that was used to kickstart this discussion, Karamat's desire for heat permeates into his political career, where he actively distances himself from his family. It doesn't make sense for him to crave heat as a politician if heat were to represent his bonds with those he loves.
Now, the largest contradiction with the idea that the temperature has relation to bonds is that Aneeka covers Parvaiz's corpse in ice. The symbolism with the aforementioned interpretation would mean that Aneeka would be isolating her twin, whereas her character arc shows that she is staying with him even in death. Furthermore, the ice melts with time, which can't be clearly explained with the stated interpretation, as the only one with a connection to Parvaiz--Aneeka--hadn't changed in the few days that the ice took to melt. Despite this, it would be incredibly odd for the temperature to symbolize progress versus stagnation, as the instances of progress depicted in the novel are varied in nature and morality, while the symbol itself--heat--is largely the same for all of the different instances. Thus, it is my belief that the symbolism of heat is a bit more specific: it represents the willingness to bring about change.
Isma's section is characterized by snow and the cold because, at that point in the story, she was content with conformity; snow was also featured when Eamonn left because he was the inciting factor in her thinking of changing, and so his departure ended that line of thought. This symbol comes full circle when Isma visits Karamat, and places ice cubes into the drinks he offers, melting the ice cubes, thereby showing her willingness to go against conformity in order to be with Aneeka, her only remaining family.
Karamat as a politician needs fire because he needs to have the drive to incite change in the populace in order to meet the needs of the nation. As an individual, Karamat craves warmth because his character arc is spent in an internal dilemma of keeping Aneeka from returning to Britain with Parvaiz. Deciphering the symbolism in his story was difficult because, despite what he says, Karamat spends his section actively disavowing heat. He rejects the notion of a higher power bringing Aneeka and Parvaiz back on wings of fire, and pulls himself away from warmth in order to compose himself. This is because he refuses to change his stance on Parvaiz, the cold reflecting his unwillingness to change said stance. Mentions of warmth are peppered throughout the story to mirror his internal struggle, not fully realized until he empathizes with Aneeka through his experience with the death of his mother.
Aneeka encases Parvaiz in ice because she refuses to allow him to change from her perception of him when they were still completely open with each other. Aneeka's section was filled to the brim with her in denial, thinking of Parvaiz as they were as children, always in sync, always as one. Parvaiz's section indicates that they had grown dissonant, especially as Aneeka decided to go to Law School, effectively leaving him alone in his mind; irregardless, Aneeka clings onto the past, unwilling to let it deviate from her memory, and so ice is prevalent in the end of her story. I can only assume that the ice is melting because realization settles into Aneeka that Parvaiz had changed without her, but Aneeka's headspace is largely unreadable following her section because she has practically no dialogue in Karamat's section, and her expressions and body language make her out to be a moving corpse, which, to some extent, supports the symbolism of ice and her belief that she and Parvaiz needed to be in sync as they had in the past.
This is my best shot at analyzing the symbolism of ice, fire, snow, and general temperature in Home Fire after about a half hour of pondering. To be honest, although a lot of ends feel tied with this interpretation, I feel that there could be an interpretation that ties all the loose ends, and I just can't think of it. It's moderately infuriating, but something I'll have to settle with for now.
As a side note, or a bonus, however you view it, my favorite "symbol" of sorts is Parvaiz's new name that he adopts in the caliphate: Mohammad bin Bagram. The word "bin" means "son of," so Parvaiz's surname is "son of Bagram," Bagram being the place that his father was supposedly tortured to death. Mohammad is the Islamic prophet, the final prophet, as it was. Putting it together, Parvaiz as he is in the caliphate was born from the suffering of his father, which is not inaccurate given the personality he adopts while under Farooq's influence and tutelage is centered around the legacy of his father. He is also the final prophet, which fits with his affiliation with the caliphate, and their forceful institution of extreme Islamic beliefs.
The name, although seemingly innocuous at a glance, gives significant insight into the character of Parvaiz immediately following his entrance to the caliphate: a boy infatuated with ideals he doesn't completely understand the repercussions of, and in the process of chasing the rose-tinted legacy of the father he knew only through a glorified legend.
Concerning more concrete symbols, I liked the lion-unicorn paperweight used by Karamat Lone, and the plastic comb used by the man from the Pakistan High Commission. They are both symbols that are easy to visualize, and both represent enforcing conformity: the lion-unicorn paperweight keeping things in place, and the plastic comb being manufactured uniformity. I do prefer the lion-unicorn paperweight though, as it also reflects Karamat's character as a politician and a side of him he believes to be idealism, plus the mental image is just visually pleasing.