Winter climbing skills are best learned on smaller peaks that in the winter become worthy mountaineering goals. I recommend that you look into the following:
Snoqualmie Pass
Chair Peak, Guye Peak, Red Mountain, The Tooth
Mt Rainier
Castle Peak, Lane Peak, Pinnacle Peak, Camp Muir
North Cascades
Whitehorse, Twin Sisters, Sahale Peak
Central
Colchuck Peak, Dragontail Peak