let me try to unmuddy the waters a bit.
anabel, and some of the other posters on this thread, are seeing "collection" and thinking you mean collection in the dressage sense, which takes years of systemic training to develop. I guessing that you're referring to collection in the same sense I would use "connection", something that's possible on a reasonably broke and reasonably fit horse, meaning that you ask the horse to move from back to front, move through it's back, and give slightly to contact with the bit, showing a little flexion at the poll.
So if that's what you mean, then yes, forward is key. If you don't have forward, when you add contact with the bit, you'll get a horse that hollows its back and slows down. With forward and relaxed, when you add contact, you should get a horse that's connected back to front. Flexing at the poll/giving to the contact is best taught, imo, separately, and from the ground, and before you attempt to ride the horse in a connected fashion.