A 13,750lb 5th wheel. MSRP $45,000 (Found one for $31,000). Man, you're jumping in with both feet!!
I don't know what kind of weight horse trailers run, but you're going to need a well-endowed tow vehicle to pull this 5-er. I suggest you read all the "towing" threads you can find on this forum. You may need to upgrade your tow vehicle.
It's going to be an expensive leap if you decide you aren't into camping. You might want to consider something smaller to start.
1988 Coleman Sequoia - popup (1987-2007)
2012 Roo19 - hybid (2012-2015)
2016 Mini Lite 2503S - tt (2015 - ???)
2011 Traverse LT, 3.6L, FWD
2009 Silverado Ext Cab, 5.3L, 4x4, 3.73
2016 Silverado 2500HD Dbl Cab, 6.0L 4x4, 4.10