Is a cyclocross bike a good option as a road winter training bike, what tyres are avaible for road riding?
Most cross bikes will work great as winter training bike. Since you don't need as much tire clearance, you might want to try a pair of mini-V brakes. I assume you'll want to ride in the rain, so putting on a pair of full-length fenders can be just the thing to protect your bike (including precious drive-train!) from grime and grit. Go a little bigger with the tires, something like Vittoria Pave or something in the 25c to 28c range.
Dawes Kalahari, Puch Prima Super Sport, Graham Weigh 853
Make sure the bike you are intending on has braze-ons for fenders, racks and bottles etc. I would use normal road tyres (well, wider than racing tyres) rather than cross knobblies. Semi-slicks are nasty on the road too.