If its not registered it won't have a (valid) license plate.. probably won't have one at all.
I recently picked up an old beat up free trailer and before doing so got a "bill of sale" form from the county clerk office. This can act as a temporary pass to use the trailer without it being registered, but is only supposed to be for situations where you just bought the trailer from someone, and can't get to the registration office immediately because it is closed. I think this temporary pass is technically good for 3 days. Here is a link to a bill of sale form, although the online one does not have the note on the bottom indicating that it can be used as a "pass" before the trailer is registered.
I had the old title (and the trailer has a VIN), and although I told the clerk I was going to cut the top off of the horse trailer to convert it to a raft trailer, I did not need a new inspection/ VIN to get it registered.
If you really want to risk pulling it without registration I would recommend carrying a bill of sale to at least have something to show to a cop in case you get pulled over.
I am by no means an expert, but did just go through the process so PM me if you have any more questions.
P.S. title and registration cost about $50, and if you bring a check instead of running a credit card you can save about a $5 fee.
P.P.S. Some county clerk offices in CO now offer appointments. You can go online to the county clerk website and set up an appointment so you don't have to wait so long when you do go to get it registered.