Post Footing Depth

I'm building a small oehler/wofati thing where there was, and still is a crumbling concrete foundation. I had decided not to bury the posts, but instead put them on concrete footings. Now, there is already a slab floor where the old foundation was where I want to put my posts...

My question is: Should I chip up the slab and dig a deep footing to frost depth, or can I just anchor the posts to the existing slab floor?

I don't know how thick the slab is, but I wasn't sure if somehow the thermal properties of the wofati would already prevent frost enough that I wouldn't need deep footings?

Thanks. Here are some pics too. BTW I'm in Connecticut with pretty cold winters