Snow on the road coming to a stop. Press brake pedal starts braking and then it starts clicking and no brakes. It almost seems there is some conflict with the transmission?? Then travelling on bare road the brakes work fine again.

Anti-lock brake systems on those old Hondas left a lot to be desired. My wife had a 1994 Honda Accord EX that she got rid of because of ABS problems. Repairs were going to be over $2,000. See if the ABS reservoir is real low or empty, which will be a bad sign. It has a clear housing--use an LED flashlight to inspect it. Fittings going into the modulator often leak on those systems. The system is under extreme pressure and the DIY mechanic can't service them. You are back to having non-ABS brakes, which will lock-up.