Up until about 2009, nearly all Class C's came with a 3,500 or 5,000 pound hitch receiver, because that's what was available off-the-shelf cheaply at the time.
Ford allows full utilization of the 20,000 (or 22,000 starting around 2007) Gross Combined Weight Rating
IF all provisions of
QVM Q-18 were followed for both the main frame modifications, and also the rear frame extensions.
The Class 5 receiver on your rig was added by a previous owner (all E-series hitches are essentially compatible), so hopefully they either verified compliance with the document above, or they had their frame reinforced if it wasn't.
Go to any rodeo out west and Class C's with 3 and 4 horse trailers are common.
The biggest issue with that particular Bigfoot coach is the short wheelbase. I think that model only came with a 200" wheelbase. This means the rear axle is already carrying more than it's share of the total rig's weight, leaving little to no additional rear axle carrying capacity for tongue weight, unless the previous owner also upgraded the tires. Some newer Class C's with the same overall length have a 218"-220" wheelbase. These would work much better for towing a heavy trailer.
40' diesel pushers might not be in much better shape, since these will be single-axle. Some of those are already over legal highway axle weights. Also, because the hitch receiver on these mounts to the engine sub-frame, older coaches have surprisingly low trailer tow limits. So, check all the hitch receiver labels before you consider an older one for towing horses.