Something related to fluids will "feel" different vs. the shift-interlock solenoid. I think first you should try to release the shift lever with the manual release.

Your owners manual should describe some kind of slot where you press a key or something, so you can shift in spite of a bad interlock. Try that, to destinguish between a really bound-up cable or transmission vs. a bad interlock that won't unlock.

 

Exactly as Jim said....the issue could be some sort of "sugar/syurp" fluid has been spilled into the shift lever (coke, sweet tea, koolaid, coffee, ect)...so on really cold days it is binding the interlock. This would cause the shifter no not move out of park.

If the shifter moves from park but the trans will not move the car,,,,,then trans fluid comes into play.

Last, the trans fluid should be changed on schedule and ONLY use Honda trans fluid.