Can I store lawnmower Li-Ion batteries in cold storage during the winter?
It would be best to store them over the winter at 30% to 60% charge in a place that doesn't get much colder than 32F/0C. Do not store them in the mower. Remove the pack for storage. The mower may draw some small current when the pack is connected.

I am not sure whether extreme cold could damage the battery. It may be OK, but I can't confirm it. That is why I am recommending 32F/0C as kind of a known safe temperature. Don't panic if the temperature dips a bit below that. The batteries don't contain water and the electrolyte will not freeze at that temperature.

The one thing you MUST NEVER DO is charge them when they are cold. By cold, I mean close to the freezing point of water. Make sure the whole entire battery pack is warmed up to around 40F or 5C before charging them. Give the pack plenty of time to warm up if you move it from a very cold area. The center of the pack may take a long time to come up to temperature. The battery charger or pack will probably not let you do this anyway, but it is the single worst thing you can do (short of outright abuse), so don't rely on the system to protect you.

Discharging them while cold will not hurt them. You can mow outside when it is freezing if you yourself are hardy enough.