There's plenty of people see such SWR problems with snow and I don't think any have provided a truly definitive answer.
If it's jumped up a lot then I'd we worried about water ingress into the antenna and check it out next time you're able. By a lot, I mean if your SWR has gone over 2:1 or more, if it's barely flinched from say something like 1.2:1 to 1.6:1 I wouldn't even worry.
(I happily run antennas from 2:1 or less
Luckily my antennas are in my loft so protected from the weather, but then I run horizontals as a typical CB vertical definitely won't fit!
Others are bound to have more input but hope that helps.
All the best,