I don't ride huntseat but I do ride dressage and western. I learned western, then dressage and back to western.
I think the thing that most W to E riders find hard is to learn to make and keep contact with the horse's mouth. Since in E riding you will not usually have draping reins, you must learn how to make contact with the horse's mouth and more importantly, how to FOLLOW the mouth ; still feeling it, but not bumping it. If your contact is not draping like western but not tight enough to be able to follow the mouth, your horse will be bopped in the mouthe each time he strides as your reins snap from a bit too loose to taut. You must have enough actual contact with the horse that you will be able to feel the horse's head rythmically moving forward and backward. That way you have something that you can feel and follow.
Eventually, you will be brave enough with the contact to not just passively follow the horse's mouth, but sometimes "hold" passively against the movement to begin to create some collection.
(of course, there's a lot more to collection than that, as ALL the dressage people will say, and they are right.)
And that's the other thing that you may find different; impulsion. English riding is based on a lot more speed and impulsion . Now, a really good western horse will have plenty of impulsion. So, let's just say for the beginning portion of learning English, learn to be comfortabel with a lot faster trot and canter. Don't panic and hold them back. Go with it.
Otherwise, just sit and ride the horse like you would any horse. The horse doesn't know or care what sort of saddle you are using. The basics are the same. Stay on, go with the flow, smile and have fun!