I apologize for the late response. I'm curious, how big are your containers and what are they made of? Did they rot or freeze?
Where I live, we do not receive snow and actually get very little rain.
When I plant my tubers (or anything for that matter), I always amend the potting soil with perlite to add extra drainage. I do this because I know that during spring and summer I will need to water my dahlias more often than if they were in the ground.
My dahlias are all planted in wood barrel planters. I don't use saucers, but my containers are all propped up using planter risers.
If your saucers are attached to the container it sounds like they're plastic? I highly recommend not using plastic planters for dahlias. Wood, stone, terracotta are preferred.