+1 to Tom and Mike.
Whether Hannigan or any Trike, choosing an apropriate Trailer can be a pickle wthout the Unit to test fitment at point of purchase. Some points that may help...
Consider your Trike as a Crate/Box. Get the dimensions (W, H, & L or D) of your "crate" from the Manufacturer which also varies by model and if the Steering Angle (Triple Trees) have been modified/changed.
Enclosed Trailers:
It's the INTERIOR width NOT the Exterior that matters.
Measure the width of the opening and floor/cargo area. Typically 3" on both sides is considered as minimum clearance so will need to be +6" or more above the overall Width of your Trike. Otherwise, sooner or later will end up with skinned paint and damaged trailer. Plus, it's a Bear to get the rear wheels tied-down properly the tighter it is on the side. But that can be overcome if so by stapping from the inside of the rims or Trike frame and cross-pulling through center to the opposite side. Actually, cross-strapping from side, through middle, to opposite side IS the preferable and most effective method of tie-down. So don't be overly wrapped up in having much more than the 3" per side clearance.
Watch the distance between the Door Cable Supports/Guides... Those can be a forgotten obstacle when loading/unloading and do a nasty number on your Trike fenders. Seen some that the Trike fits into but had to have a person on each side to pull the cables out and clear of the fenders during entry and exit. Can be done but not optimal or desirable every time.
Be sure and consider any interior wheel-wells that protrude into the cargo floor area. Measure the distance from where you want your center of rear wheels to sit to the rear edge of the protruding wheel-well. Compare to your Trike (call Manufacturer) to get minimum distance from rear wheel center to front edge of trike fender to be sure that Trailer config will work. The rest of the trike forward of the front fender is a non-issue as concerns the Wheel-wells. Just be sure there is enough floor area rear of the wheel-wells to accommodate the rear body section of the Trike and still be able to close the door. You can also work that backwards and go from where the front wheel of the trike must sit to the rear edge of the Trailer wheel-well then compare to the Trike from the front wheel to front edge of Trike Fender.
You must also make sure to consider where the Trike placement in the Trailer needs to be to be properly Load-Centered when taking the above measurements. An improperly load-centered cargo within a Trialer makes for a nasty & frustrating trip/pull and can be overly taxing on brakes, tongue, coupler, hitch, etc.
ALWAYS get a Front & Side Man-Door! If you don't, hope you like to climb from the seat over the rear of the Trike to get out.
The Short of it: As Mike's pic and experience clearly show and prove, virtually ANY 7'x12' enclosed Trailer will suffice and do nicely for ANY Trike. Most of those will be designed so that wheel-well placement will not be an issue for the Trike and how it needs to be positioned for proper load-centering. You can use the above to verify should you be so inclined.
Open/Flat-Bed Trailers
Pretty much same as all above but a tad more forgiving. Then it's just the floor and the ramp width that must accommodate the Trike dimensions and will not require much extra.
Just watch the side-rail height (if has sides but most do).
Also consider if Ramp-Gate equipped as that MUST be able to be lifted/closed and locked up and clear the Trike rear.
As such, ANY 6' by 10' Open/Flat-Bed Trailer will work. 10' may be close but as the longest Trike is right at 118" (w/Mod'd Triple Trees) from extreme front edge to rear, so 120" will definitely accommodate. If that is cutting to close for comfort (1" to spare front and rear) for you, go 12". Along with that, the widest is right at 62" (actually 61.5" with a +/- of 1/4" as Tom pointed out) so a 5 & 1/2' (66") Trailer will work and is somewhat as common as the 6' Trailers are. So, you can actually look for a 5-1/2' x 10' Open Trailer and you should be fine. A 6' x 10' will Definitely get the job done with NO issues at all.
Again, be mindful of the inward protruding wheel wells as they relate to the Trike and where it needs to sit in order to ride and haul correctly.
Tie-Down points are also obviously much less, if any, of a concern on Open Trailers as well.
The standard U-Haul Trailers Will NOT work. You must specifically request a Car-Hauler Trailer from them and as Tom said, Those usually are few and far between, hard to locate, and as rare as common-sense in D.C. I have seen people who have requested those and were given a Cargo Trailer with 3' metal sides instead. A Bitter Pill to swallow when arriving to take delivery. Be caredful dealing with U-Haul or the like. Take a tape measure with you when you go to pick it up and verify fitment.
Hope this clarifies and helps you and any others with the same concerns out in Trike-Land.
or, as others have said (and I agree 100%),,, Forget about all this Trailer Crap and
RIDE THAT RASCAL HOME