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