It's not a new law, but merely a law that they are enforcing now. Here's a cut and paste off of the BLM website;
Does my OHV have to be registered?
While being operated or transported on public lands or roads, OHVs must display a current OHV registration sticker. Off-highway motorcycles may be registered as street legal, if they are safety inspected and insured, or as off-highway vehicles. Obtain registration from the Utah Division of Motor Vehicles. If you are a nonresident visiting Utah please click here.
You may renew your OHV registration online at:
http://www.utah.gov/rapid
Your OHV is registered by its manufacturer-assigned vehicle identification number. The Division of Motor Vehicles will issue registration base decals to be mounted in a visible location as follows:
Motorcycles - on each fork.
ATVs - On front or rear of the vehicle.
Snowmobiles - On both sides of the hood pan or tunnel.
All other off-highway vehicles - On the front and rear of the vehicle.
Off Highway Vehicle registrations expire annually on the last day of the month that the OHV was purchased. Annual registration fees are currently set at $14.50.
I spoke directly to (remained nameless) of law enforcment to dispell all the rumor control going around about trespassing and verified that this was in fact what they were writing citations for (no registration). That person (to remain nameless) even elaborated to the fact that they were strictly enforcing it due to the growing trend of trailered vehicles that were obviously not street legal hitting the trail and wanting to ensure the safety facture.