In reply to Frank4short:
I've got a spaniel who actively rummages about in the undergrowth, and we have alread lost one coat.
The most effective thing to do is get a tub of really cheap nasty marg, and very lightly (ie, rub grease into your hands then rub them over the pooch) grease the dogs' paws (especially between the pads) and their under carriage- tummy, feathers, armpits JUST before you go out; any earlier and the dog will simply sit and proceed to lick it all off!
when you get in from your walk, the dog will happily sit and clean itself up, if there's any grease left.
the problem with allowing the snow to accumulte is that it tends to mat up, twist, and then get ripped out by the weight of the snow and the dangly movement of the balls- painful. when the snow really compacts, it's hard to get it off, and a couple of years ago I had to literally cut the stuff off, losing some of the dog's feathers as I went. After that I deliberately trimmed back some of her fur and then took to greasing her up.
Sx
PS same trick works with preventing snow from balling up under the hooves of horses- whack a load of grease into the hoof.