Pitcher wearing first baseman's glove
 

FED Rule 1.3.6 details glove requirements and sizes. Except for the catcher, there are certain dimensions that must be followed. As far as I can tell, first baseman's mitts as currently advertised in sporting goods stores fit those requirements just fine and can be worn by the pitcher (which was a point of discussion with some people).

I'm asking about the past. Was there a point in time where this was not legal? If so, can someone identify about when the rule changed?

Been legal since 1992 that I know (maybe a real old guy can go back farther) I however have never saw a player besides the 1B man and Catcher wear a mitt. Stupid rule.

I have but only at sub-HS levels, usually when the 1B comes in to pitch. Then the coach comes out and say "he can't use that glove" and we discuss why he can. I'm not even sure of what the difference is between a glove and a mitt myself. Is it no separate fingers in a mitt, like a mitten?

Yes.