I agree that the panel is to small if the battery is being used at all.

I have a few 10 watt panels that I connect to batteries that have a slow discharge from vehicle clocks and such and they work perfect for that, but I would not expect them to charge it in the winter.

The $30-50 option is to buy a 2nd solar panel.

My neighbor has a Mule opener. The battery lasts 2 years. His issue was not enough charging capacity vs. times the gate was opened. I added a second 20 watt panel and a deep cycle battery. I also buried the battery in a battery box almost to the top. That stabilized the temperature.
The battery charger in his unit was made for bulk charging only. It never reached float. So, occasionally when he was waiting at the gate for the school bus, I had him apply a quick charge once a month. So far that battery has lasted 4 years.
BTW, a fully charged lead acid battery will not freeze in -50 deg F.

About diodes
 

The 1N4004 is a silicon diode, it's a member of the 1N00x series of diodes 1N4001 has a peak inverse voltage (PIV) of 50 volts, the top 1N4007 has a PIV of 1000V, silicon diodes have ~ a .7 volt forward voltage drop (insertion loss). I buy these diodes by the hundred for 7 cents each, I always buy the 1N4007 because they work in ANY application calling for a diode in the 1N00x series.

At one amp, which these diodes are rated at, the drop will be .7 volts across the diode.

Shottky diodes have much less insertion loss, a 1N5819 has about a .25 to .35 voltage drop under load but the schottky diode has higher leakage than silicon diodes. For PV's you must put a diode in series with the battery or the battery will discharge into the module. For low current applications you can use a 1N5817 or a 1N5819, the 1N5817 has a lower PIV, the leakage is low enough on these diodes that the module won't drain the battery at night.

Rob