I ama mom of 2 year old girl and 7 month old boy..
I found lots of things for us to do this winter.
Ferndale community center has a playroom open 9-3 mon- friday. Lots of toys fairly clean. $ 2 a kid.
Roseville has a gym that they open certain days.. You should be able to find it online. I have never been there.
Centerline schools has "play with me" on tuesdays and thursdays. A playgroup for kids 0-36 months. It costs $20 a month. We go to this program. You can bring your infant with you. You should be able to find it online...or send me an email and I can send you a link
Look into musical story time - classes start this week in troy and rochester, royal oak and madison heights. It is a great class. We go to the troy location on saturday mornings... the website is musicalstorytime.com
oakland malll, great lakes crossing and lakeside have playareas for free.