Here's the usual remedy....... rubber hammer the solenoid to free it from sticking especially in cold weather. If you want to prove this is source of problem ask your assistant to turn the key while you hammer away at the solenoid..... otherwise you can rap the solenoid yourself and then should be able to start the car as one man operation..... a cheap skate friend of mine with really old BMW suffered sticky solenoid problem and carried rubber hammer in his car 2 yrs before actually replacing the starter/solenoid unit - Itsa common problem.

If the solenoid is inaccesible with rubber hammer, get a baseball bat or 2x4 and use it like a two fisted pool cue or act like Capt. Arab harpooning the whale as you smack the solenoid in just the right place, dont worry about hitting it too hard..... with time you can perfect the technique to make it through the Winter - and then maybe the problem will go away in warmer weather.