I think it really depends on the individual store. I know lots of people take dogs to Lowes and Home Depot, but the Lowes here will NOT allow dogs, no matter the size, even in the garden department and will quickly ask you to leave. So even those are not universal across the board.
I would suggest that you just call and ask in advance.
Even then, it may just depend on who you talk to, but it's the safest way to check I would think.