Most full size trucks equipped with a tow package should be able to pull a standard two-horse bumper pull in normal conditions. I haul mine with a 4.6L V8 Tundra double cab. I feel it when I tow up to the state park for trail riding (it's on the top of a mountain, so a pretty steep drive), but barely notice it's there when I haul the hour to lessons twice monthly (mostly highway).
If you live in a very mountainous area or might be traveling on less-than-ideal roads, want to tow a gooseneck, or other special situations, then a bigger truck is probably warranted.
“The horse is a mirror to your soul. Sometimes you might not like what you see. Sometimes you will.” - Buck Brannaman
"Nothing forced can ever be beautiful." - Xenophon