Is it possible to attend grad school in cognitive sciences without a medical degree?
At least in the US, a neuroscience or cognitive science PhD program generally admits people with undergrad or masters degrees, which generally can't be medical degrees since many US schools do not offer medical degrees at those levels.

So the answer to your first question is yes.

As for the specifically a math background, I expect that most schools would consider such an application. Even in fields that have corresponding undergrad majors, it's not uncommon for people to enter PhD programs from very different undergrad studies. An application would have to address the question of having an adequate background and understanding of what the field is like.