What's the lowest temperature to ride, without causing damage to your battery? Is it also safe to use insulation??
Assuming it's a lithium ion battery, using it in low temperatures will not cause damage. Capacity will be reduced though. The battery management system will (or should) detect if there are any weak cells, and disconnect the battery pack before the cell voltage gets too low. A typical symptom of that is one minute the battery will show a healthy charge status, the next a low battery warning or even it cutting out. This is most likely to happen to an old battery or low quality battery in the cold. Going up a hill when it is cold is when the battery is under the most stress, and this the most likely time for an old or weak battery to fail on you. Insulation is likely to be of marginal benefit, unless it is for a short journey.
Recharging it is another matter though.
Do not recharge a li-ion battery when it is below 0C. This may cause metallic lithium to plate out, which significantly destabilises the chemistry (as in: fire!). Wait until it has warmed up - and remember that though the casing may feel warm, the cells inside may still be cold.