I brought two saddles to Mongolia with me, and packed them both with clothes and other things as part of my checked on luggage. I flew Aeroflot and paid about $300 for excess baggage fees (saved a little thanks to a friendly guy at the counter in LAX). I came in to Chinggis Khan International with 9 giant suitcases and miraculously escaped any customs fees, since the customs agents weren't convinced that all contents were my own. They were, so maybe that worked in my karmic favor.
I'm sure you've already thought of this, but Mongolian horses have relatively small barrels and narrow withers. I have my all-purpose Pessoa here, that I got a pony sized girth for, and plenty of saddle pads. I also brought a fairly large charro saddle for my husband. That saddle will only fit one of the horses in the family's herd - a larger Russian horse. You could consider leaving a pack saddle at home since there's a just as efficient Mongolian version. That might help lighten your load.
Bridles could also stay at home, unless you have some pony sized bridles, but Western/English bits may take Mongol horses some getting used to. They use a generically sized loose ring snaffle type bit here, and the horses do just fine with them.
