@Halfwaythere,
I wouldn't mind getting a quick message from an ex girlfriend.
Depending how I felt about her, I might ignore it (and in that case I wouldn't want to get a second message). Or I might answer politely and dismissively (in which case I probably am being nice but don't want anything from it). Or I might offer to get together for coffee (in which case I want some sort of connection).
So, I don't think it is wrong for you to send a quick message.
A few warnings though...
- There is no such thing as "closure" in a dead relationship. If you are looking to fix anything emotionally, or to clear up a bad taste... you are just looking for pain. The relationship is over and he has moved on. Leave it in the past.
- He has every right to ignore your message. You shouldn't take that personally (after all the relationship is over for both of you). Don't get your hopes up. You might get an angry response. You shouldn't take that personally either.
- If he wants to talk to you, leave the past in the past. Whether you want to be facebook friends, exchange Christimas cards, or start something new, it is all the same. You can't fix up a relationship that ended. Sometimes you can have something new.
So, sure. Send the message if you want. Accept what happens and make sure that you aren't looking for closure.