It is a matter of not staying out to long and drying the bun properly after. Many buns also want something they can sit on in case the snow feels a bit scary to begin with. A folded blanket would do. Some buns appreciate snow, other buns seem very suspicious of it. 

Mites and fleas are not very active in snow. I have mosquito netting around my outdoors run that I use in the summer. In places where there is a high risk of external parasites, Revolution (selamectin) can be given regularly as a preventative measure. Revolution is bunny safe but you need a vet’s prescription.

(When we’re discussing anti-parasitical for buns, we always issue this warning: Never use any anti parasitic containing fipronil on a rabbit. Fipronil is sold under many brand names, f ex Frontline. It’s deadly toxic to rabbits, but fine for cats and dogs).

Another option is to bring the outdoors inside. I’ve seen lots of posts of people filling a shallow container or bathtub with snow for bunny to play in. The one time I tried this with my boys, they were confused and annoyed by the cold snow.

As already said, it depends on the bun. In my experience, most of them love it (its fun to dig in). I put snow in the hutches sometimes for them to dig in, and they think its the best thing ever. They ate it, too, which was kinda weird, but its water, soo… But, yes, be sure to dry them off thoroughly after letting them play outside.