Add outlet to existing outdoor UF cable
This should be fine. A couple caveats:


You'll need at least a foot of slack. One trick is to use two junction boxes--the first to extend the cable, adding slack, and the second for the outlet. Think it through before you cut so you don't end up short anyway. All junction boxes need to remain accessible (not buried behind drywall).
Use pigtails rather than receptacle passthrough (or, worse, the backstab ports). You don't want to run a potentially heavy current between the same-side screws on an outlet if you can help it. Doing so adds extra points of failure for the downstream portion of the circuit. Bring the source wire, the downstream wire, and a jumper for the outlet together in a suitable connector, such as a yellow or red nut. 
Use a large enough box for the outlet and those pigtail connections. A full-depth (17 c.i.?) single-gang box would be fine.