This service bulletin was for the 1st gen Rincon...
"TRX 2003 TRX650FA Rincon
Cold Weather Transmission Performance
When used in cold regions, the TRX650 Rincon must be brought to normal operating temperature before usage. This model uses motor oil in the automatic transmission, which requires some time to normalize the flow characteristics. Additionally, oil viscosity is very important to the proper operation of the transmission. If a customer has a problem with shifting or climbing performance,make sure he is warming the unit up prior to putting demands on the transmission.Also make sure he is using the correct viscosity oil.Refer to the owners manual for specific recommendations.Do not use oils with graphite, moly, or "energy conserving" oil. Honda offers 5w-30 oil for use in cold climates. Use 0w-30 oil if operating the unit below 10 F. Some aftermarket oil manufacturers offer 0w-30 oil.
Warm-Up Guidelines
The TRX650FA employs a torque converter type transmission that uses engine oil as the working fluid. To avoid any possible transmission slip due to insufficient oil in the torque converter, make sure you and your customers follow the warm up guidelines listed below.
Air Temperature (50-95 degrees F)
Normal warm up--until the engine runs smoothly and responds to the throttle with the choke knob in the fully OFF position.
Air Temperature (5-50 degrees)
Warm up the engine for three minutes.
Air Temperature Below -5 degrees F
Warm up the engine for five minutes."
Obviously, it wars carbed, and i am sure there is a newer version around, but it should give you a good ideal of what sort of warm up times are needed. I agree with HondaSxS...unless you are in Siberia, your times do sound long.