Small Engines (Lawn Mowers, etc.): Starter, toro wheel horse, polarity reversal

Question
I have a Toro Wheel Horse, about 7 years old, with a Kohler 16 hp vertical shaft motor. Started last week, and then I went to start it on Saturday and had no luck. Bought a new battery, had solenoid checked, ended up determining that it was the starter motor. I bought a new starter and went to install it tonight. The starter does turn, makes a whining sound, but will not turn the flywheel. The flywheel does turn by hand, but it seems that the starter gear is not engaging. Could it be the engine needs to be turned with the spark plug removed to get the starter to engage or is there some other trick or technique that I need to use to get the starter to turn the engine? Also, I live in Upstate NY, and it's pretty cold here now, about 20 or so. Should I warm the mower first? As I said, I had it running on Christmas day with NO problem, other than the starter was a little balky. Any help would be appreciated.

Answer
Is the battery connected backwards?  Laugh, but I know for sure the starter will never turn the engine if the battery connections are reversed.

If the battery is connected correctly, watch the starter turn.  The pinion gear should raise up engaging the flywheel ring gear.

Check you battery connection and make sure the battery has not reversed polarity.  The polarity reversal is rare but we had a couple of batteries reverse polarity last year.

Let me know what you find.
Eric