Well, that depends on how confident you are in your charger and timer. I use both the Battery Minder and Battery Tender Jr's in my world and have confidence in them both. Failures could be costly however. I would not have the same confidence in my standard chargers, but does that mean that my confidence in the others is misplaced- I dunno.
If I were leaving for the winter, I think the best piece of mind would be to leave it unplugged. The battery should be fine anyways. If your battery isn't nurtured to its fullest and it dies a year sooner- you aren't out much.

You didn't mention any brand etc. so that leaves some doubt as to proper procedure for YOUR mower.

I seem to have read about some types that recharging is only for a gas engine with electric starter.
IF you aren't starting it, you really don't need to recharge it.

Personally, I would just charge it up and then leave it.
I wouldn't leave a potential fire hazard plugged in.
Peace of mind is worth a battery potentially going bad IMO.

Else can you store it at a neighbors and have them tend to it, IF it's a different system?

Bring the lawnmower in the house? How about just the battery? If it's that important I would remove it from the lawnmower, charge it up and leave it in cool dry area on concrete or wood to protect the floor in case it leaked alittle.