any saddle will do as long as its a really good fit and comfortable for the rider. Mine are in Albion K2 jumpers but i have hunted in everything from an Ideal Jessica dressage to a WH show saddle upto a Stubben Siegfried MFS double blocked (my absolute favourite!)
You need a saddle with a decently padded seat unless you have one yourself! Your bum will be in it for hours. Watch out for knicker-line-blister-syndrome too!
You don't want too high a cantle if you are going to jump drops at speed - you'll end up sitting on it and that can hurt.
It needs to be big enough. There's a fashion for cross country saddle seats to be quite small, but you aren't going to be standing in your stirrups for 5 minutes, you're going to be sat on your bum for half an hour at a time.
I use a WOW event seat, which is almost completely flat but nicely padded, with show jumping flaps on the forward position. My horse loves it too as it has a carbon fibre jointed tree and swings with his shoulders. And the air filling moves as he does, so he gets no pressure points from being in it for hours at a time.
We use Stubbens - very hard wearing, stand up to thorns and rain pretty well. We use a siegfried, a parsifal and a daland - all jumping styles and pretty comfortable even after a day sitting on them!
I use a Thorowgood T4, a GP, which is one of the cheapest saddles on the market, but it fits my cob well and I find it very comfy. So no, you dont need a specific saddle.
I use my kentaur, a.) because it fits everything and b.)its very much styled for jumping. However have hunted in everything from a Antill gp, to an old-fashioned hunting saddle- very flat!, to Thorowgood gp's.
As long as it's comfortable it doesn't matter, and as cptrayes says dont have one with too high a cantle as jumping over a big drop fence and hitting that is not pleasant.
I use a wow XC saddle with a shallow seat, but then that's what fits him best and its about the most comfortable saddle I've found. we don't do that much jumping out hunting, but we do quite a lot the rest of the time and I can only afford one saddle!
My fav is my John whitaker, it really fits me tho and feel secure in it, hunt my bigger horse in her pessoa tho, which is also good but prop not quite as padded but only got those two saddles and only really started hunting this year was more into showjumping before, but do prefer a jumping saddle as means I can ride shorter and knee rolls are more padded, and obv designed for jumping!!
did my 1st season in an old VSD but got an Albion K2 jump this season and it's saved my bum a fair few times now! last season i fell off 5 times - not gonna say anything to jinx myself about this season but the knee rolls are amazing! i did have to put a seat saver on it though - it was so hard compared to my old saddle!
One thing I would say which is sort off about saddles is too make sure that u still have plenty of holes left on your girth straps left as u will often find that u end up tightening them 1/2 holes more than normal during th day!