What kind of vehicle/horsepower will I need to tow a Bobcat 322 mini-excavator?
Guidance from, say, Bobcat is pretty thin. I saw one web post from a bobcat dealer in which the advice was "Make sure the vehicle is adequate to tow the bobcat". Yeah, no kidding Sherlock.
The Bobcat plus the trailer weighs about 4000 pounds. What kind of vehicle will I need to tow this?
You'll need something with a Class III hitch to handle the weight of the trailer. Odds are good that if a Class III hitch is available the payload of the vehicle will handle the tongue weight, but make sure of that. I would expect the tongue weight to be upwards of 600 pounds. Depending on the vehicle, you might want to look for a weight distributing (equalizing) hitch.
Horsepower requirements will vary with the terrain and acceleration requirements, but it's quite likely that any vehicle for which a Class III hitch is available will be up to the task, at least in relatively flat country.