To some extent that’s a problem that can’t be solved. You’re working hard and essentially have strapped a big wad of insulation to your back. So sweat, and lots of it, is inevitable. Many years ago I had a Gerry rucksack that had a backpad made of wool felt. I might as well have strapped a sheep to my back.
Still, there are ways to mitigate the problem. For one thing, you should ensure that your layers can dissipate moisture as rapidly as possible. I’m a big fan of Polartec Power Dry, which I’ve been wearing a lot this winter. It’s great at wicking away moisture, thanks to a two-layer design that has a textured inner layer to vacuum up sweat and carry it to the smoother outer layer. There, it simply spreads and evaporates. REI makes a good long-sleeve piece with the stuff, called the REI Power Dry Zip T-Neck ($36). It’s a great basic base layer for winter sports. I also like Patagonia’s Silkweight Capilene, such as their long-sleeve crew ($40).
In olden days, when I had that Gerry rucksack, I also occasionally wore a mesh T-shirt, something like Wiggy’s Fishnet Long Underwear Top ($33). It’s made of nylonnot ideal because nylon can also soak up quite a bit of moneybut the idea is absolutely sound: create little air pockets next to your skin, so sweat has a chance to evaporate before seeping into your clothing.
At the other extreme, you could always shop for a backpack or daypack held as far from the skin as possible, so the air can circulate. The North Face Patrol ($199), for instance, is a ski-centered pack with a breathable foam back pad. The Marmot Moose’s Tooth ($179) is another winter-oriented pack that has a very fast-drying, well-ventilated back pad.
Check out the REI website for the recommended by the Gear Guy.