Tom Brady's son got a rude awakening on where he stands in the family pecking order today ... when his parents kicked him out of his comfy stroller ... in place of the family dog.

Tom and Gisele bundled up to brave the aftermath of the Boston snow storm today ... and took a family stroll with their son Benjamin and pit-bull Lua.

But it seems like Lua -- despite her custom winter doggie jacket -- got some cold paws on the walk ... and his 4-year-old son got booted from his all-terrain stroller in favor of the pooch.