I've done it often, little gravel, medium gravel, dirt trail, snow. Yeah snow...
It's fine as long as you don't get into bigger gravel. Anything too deep will cut sidewalls or ding rims. (And that sounds painfull....)
And careful riding in the snow. Following a dirt path near loveland ski area in mid spring, in the woods wearing just light gear. I realized a few mile back that if i flatted i'd be walking in cycling shoes and spandex for half an hour and likely freeze my butt off...
Funny, i pulled into the coffe shop in Idaho Spgs next to a guy in ski gear. He'd been boarding the pass right above me. Weird meeting...