Not a simple Yes/No question. Lots of things to consider....
1. I do not run my mower from October to April here in Georgia What I have found is that I do NOT need to maintain my Exmark mower battery... IF I use a battery disconnect device. This because the main discharging path is through the diodes of the rectifier, so the battery MUST be physically disconnected during storage.
Link To Battery Disconnect
2. However, in Georgia we do NOT get into extended periods of freezing temps. We are usually in the 30-40F at night; then we'll have about 20 nights total in the 20F zone. My mower and battery are kept indoors, out of the wind and rain, but NOT in a heated or insulated space. Cold lowers the specific gravity of the battery, which can lead to physical conditions conducive to battery sulphation, which is death for most common types of batteries. Colder climates will call for different types of action.
3. One of the results of intermittent maintenance charging is to raise the internal temperature of the battery. This might offset freezing temps, but if used too much can also "cook" the battery to death. Batteries do NOT like constant maintenance charging, nor do they like being kept at "full charge". Additionally, in my professional experience most of the "maintenance chargers" being sold are charging at a rate that's far too high. (I know Yusua recommends an intermittent charge rate no higher than 1/10th of the AH rating. That means ~1/2 to 3/4A [500mA to 750mA].) This means a charger needs to be fairly technical in order to remain connected 24/7 and not to "cook" your battery. If you can't afford a $70+ battery charger, then the next best step might be to use a lamp timer set to allow the charger to be ON for only 30 minutes a day.
In short: 1) disconnect the battery, 2) keep the ambient temps between 40-60F, and 3) limit the duration AND charge rate if you must charge.