Don - Southeast Texas is currently experiencing temps of 70-80°F. Unfortunately, animal pelts from our area just don't measure up to their northern cousins. Also, retaining the pelt of a fur-bearing animal for any reason requires a trapping license; whereas the removal of nuisance animals doesn't.

Stickem - Conibear traps are the way to go for both otter and beaver. Leg-hold traps will work when using drowning cables, but otherwise have several drawbacks when targeting aquatic mammals.
I caught 8 otters in one pond over the course of one month last December (5 in one evening) while also targeting beavers that were burrowing into the levee. The otters' presence was noted by numerous partially eaten bass and catfish carcasses. Seems their preferred diet changes from crawfish during the more temperate time of the season to fish in the winter. The bucks appear to roam solo, while the females and juveniles move from pond to pond in groups.
The most successful sets were Conibears placed (submerged) at beaver-den entrances; which otters regularly investigate. Placing a submerged Conibear at entry/exit points works well too, especially when the pathway is "channeled" and the trap is placed directly beneath a partially submerged log - which confines the animal's route through the trap.
Be sure to condition (boil) the traps and allow them to take on a light coat of rust before use, since this seems to help eliminate some aversion to the trap's presence.