Road cycling can certainly be cheaper but MTB especially lift served is expensive. I spent $1k on my downhill bike and that was the cheapest bike I could find that was safe to ride. Then you through in the costs of flats, each tube is about $15. Then if you have a really bad crash and break something it starts climbing. Don't forget about fork rebuilds and having your biked tuned up at the beginning of the season. Then there is all the extra gear, full face helmet, body armor, shoes, DH shorts, jerseys, ect.
Then if you get really into it you can absolutely have a quiver of bikes just like skiing. Downhill, Road, Pump Track/Dirt Jump, XC, Track, Fixie, ect
I posted this in the bike stoke thread but here's a pic from my living room and this doesn't have all the bikes my roommates and I own in it:
In case you don't notice there are also bikes in between the ones on the racks.
I don't think I have ever spent more then $600 on a pair of skis including bindings, most have been less then $300. Just like with cycling you can get by on a single pair of skis you don't HAVE to own a quiver, you could pick up a pair of straight skis for $20 bucks from a thrift store and ski on them, not really any different then buying a used walmart bike for $10 from a garage sale.
I think it really just depends on what you choose to pour your money into. Both can be very expensive