Cheri,
If by "long underwear for snowboarding" you mean some of those old style cotton blend waffle "thermal" underwear- then I'd say that is not a good choice.

Try investing in some baselayers made of 100% thin merino wool. Both SmartWool and Ibex brands are good examples. This stuff will be soft, keep you WARM, and yet be breathable. It also does not incubate body odor after one wearing like polyester and cotton does, so you can wear it 5 or 6 times before washing. You can wear the tops any time, not just for biking. They won't look weird like those goofy polyesther jerseys can.
Wear a longsleeve merino crew neck top underneath a turtleneck one- total toastee!

Also try a long warm tight over your biking shorts instead of the long underwear.
Some ski socks will go up to your knees either under or over your tights, and keep your lower leg and foot warm. Or try some leg warmers made for biking (tuck the tops UNDER your shorts legs).
Get a good neck gator in merino wool and you can pull it up over your mouth and it will not get soggy or cold as you breathe through it. Get a thin merino helmet liner (se TE's SmartWool version- I have it and it's perfect, and covers my ears as well!) to keep your head warm.