Possibly Glen Duncan's 2003 novel I, Lucifer.
From the Amazon link:
The End is nigh, and the Prince of Darkness has been given one last
shot at redemption, if he can manage to live out a reasonably
blameless life on earth. As a trial run, he negotiates a month of
"trying without buying" in the body of struggling writer Declan Gunn.
("Incarnation, the angelic drug of choice. Unlike cocaine, not to be
sniffed at.") Luce seizes the opportunity to binge on earthly
delights, to straighten the biblical record (Adam, it's hinted, was a
misguided variation on the Eve design), to celebrate his favorite
achievements (Elton John, for one), and to try to get his screenplay
sold, but the experience of walking among us isn't what His Majesty
expected: instead of teaching us what it's like to be him, Lucifer
finds himself understanding what it's like to be human.
I don't see any reference to snow in Hell, but maybe you're thinking of this passage in chapter 26:
I never really wanted this job. (As all dictators whine.) Trouble was,
when we found ourselves in Hell everyone looked at me. (How to
describe Hell? Disembowelled landscape busy with suffering, incessant
heat, permanent scarlet twilight, a swirling snowfall of ash, the
stink of pain and the din of . . . If only. Hell is two things: the
absence of God and the presence of time. Infinite variations on that
theme. Doesn’t sound so bad, does it? Well, trust me.)