The CX-5 will not disable AWD due to cold (only overheat condition). A number of us owners have driven to zero degrees and below without issue. 15F is not very cold.
The CX-5 has amazing self-diagnostics. The AWD diagnostic checks inputs from the AWD temperature sensor and checks the function of the AWD clutch solenoid. If any of these tests are out of range it will illuminate the AWD warning light and disable the coupling to the rear wheels. This diagnostic function has a memory and will not self-clear even if the battery is disconnected or the original fault is no longer present. It could be as simple as water in one of the connections causing a temporary out of spec condition. If it were not under warranty I would remove both AWD housing connectors (temp. sensor and AWD solenoid) inspect for damage, spray with electrical contact cleaner followed by dielectric spray grease, reassemble, and clear the code using an inexpensive OBD code reader and see if the error returned.
Was this over-flowing creek you drove through brown by any chance? Clear I've driven through clear water many times without issues but brown water is more electrically conductive. In any case, if you're going to be driving through water (in any type of vehicle) you need to step up the maintenance on items like wheel bearings, brake fluids, electrical connectors, etc. Most off-road manuals will instruct to replace fluids after driving through standing water. I'm not saying this was preventable, just that water causes more issues than most people realize.
I spent 30 seconds crossing an over-flowed road and it was roughly as deep as stated ground clearance spec. This should not be an issue.
A flashing AWD light indicates a condition that is transitory and will self-clear if/when the error condition is no longer present (for example, over temperature AWD fluid). A solid light disables the AWD coupling so driving it is not an issue (assuming you don't need AWD). Old school cars did not have a plethora of sensors and diagnostics so we would never know if there was a fault unless/until it manifested itself in more obvious ways. People get freaked out about dashboard warning lights but they are typically just minor faults that we would otherwise never know about.
That's fine. As long as it's not grinding anything to death, it can wait.
I'm amazed my Mazda has never thrown a single fault code in over three years of all types of usage/environmental conditions. My Volvo was overly sensitive in this regard starting from day 1.