no, that's not really correct at all. i think you may be confused on the difference between commercial tags and weighted tags.
a truck pulling a 32ft. camper is 100% illegal with a standard tag. a weighted tag is definitely required, the only question is how much. a standard tag barely covers the weight of most trucks themselves, and in the case of 3/4-1 ton trucks it doesn't even do that.
a minivan on the other hand, or any other non truck vehicle, can pull whatever it pleases on a standard tag and is 100% legal (as far as tags go, anyway).
even assuming you meant to say commercial tags instead of weighted, there are several criteria in addition to and independent of weighted tags that have to be met before commercial tags are required. simply pulling a certain type of trailer (i.e. two horse) is not a sole deciding factor. weighted tags were created to bridge the gap between private and commercial. a way for the state to tax higher than "normal" use of the infrastructure while still maintaining a somewhat clear line between private and commercial.
