The polite form (丁寧語 teineigo), also frequently referred to as です・ます調, is used for making everyday speech more polite across the board.
Honorific language (尊敬語) and humble language (謙譲語), also frequently jointly referred to as 敬語 keigo, are used to elevate someone else or humble yourself, respectively. (Honorific and humble language are usually used in the same register, i.e. think of them as one "set".)
Usually keigo is used in combination with ("on top of") teineigo, but it is possible to use one without the other.
When learning about Japanese "polite" language, keigo and teineigo are often jumbled together, but it might be useful to consider them independent.
To answer your question, it would be unusual to use honorific or humble language when talking about snow, but it is very appropriate to use polite language, so
is perfectly natural (and you might want to write the whole letter in teineigo).
As @l'électeur notes, the sentence on the whole is not 100% natural. I'm not quite sure what exactly you want to say, but here are two possible scenarios:
beginning of winter
Today it is exceptionally warm and the snow is slowly melting.
end of winter
Today it is already quite warm and the snow is slowly starting to melt.