Typically a 6 volt solenoid, or starter, will work nearly as long, if not longer, than a 12 volt will, when used on a 12 volt system. My go to guy at our local rebuild shop told me this years ago when we had the starter on Dad's 440IC Deere rebuilt. We had taken the starter in to get the start switch replaced and asked him to check out the starter (ie change the brushes, replace the bearings, etc) while he had it. When we picked it up he asked wether we were running it on 12V or 6V as the starter was wound for 6V. At the time Dad had had the machine for nearly 10 years, and it had been converted to 12V long before we got it.
What he told us was the insulation on the 6V windings was heavier than what was on the 12V. As a result it could withstand the lower amperage necessary when running on 12V where a 12V starter didn't have the necessary insulation to handle the higher amperages necessary to run on 6V.
Like I said we were told that probably 10 years ago and Dad had had the machine for several years already at that time. So, right or wrong, a 6 volt starter had worked just fine for us for over 10 years with absolutely no problems, and I'd have to assume that the coil on a solenoid would do just the same. The only thing is that with 12V to a 6V widning, it would tend to pull in harder, which may or may not shorten it's life.