While I am a July bride, I had to send my invites out way ahead of schedule because it's an international wedding, so I can't really give too much advice on timing.
What I can tell you, however, is that with a 2-3 month time period between sending out invitations and the RSVP deadline, people are going to forget. We did the same thing: Handed out invitations while in the US in late November, set the RSVP date for mid February. Exactly 3 out of 93 people didn't need a reminder – everyone else missed the deadline. People got the invite, were happy about it and had plenty of time to make plans. Only they knew the RSVP deadline was way off, so they postponed getting back to us and in the end forgot about it.
Obviously our situation is somewhat unique, but I can still only advise against letting too much time pass between invitations and deadline. Unless you don't mind chasing everyone's RSVP down in the end – which I found pretty frustrating, although I totally understand why this happened.