Lead acid batteries only freeze in the cold if they're discharged, say near half capacity. E.g. A lead acid at ~40% will freeze at just under -20 C. On the other hand, a topped off lead acid won't freeze until -60C (+/- for different lead acid technologies). So if you find your battery is 'dead' after storing it outside, it's because it died then froze. Consider replacing a battery that has froze solid as it most likely internally ruptured.
If you're storing a LiFePO4 for a couple weeks-months (without any load), it's recommended to actually bring it down to 40-60% capacity even for cold storage (you're data sheet will say exactly) but make sure it is warmed to operating range before putting a load on it. Depending on the charger, if it can't account for the cold (although it sounds like yours does with the -20C rating) then it will charge it as if it's room temperature... then when the battery actually warms up when you bring it into a warmer room it's voltage WILL increase and damage the cells. Your better off charging it at room temperature (give it time to warm up first before starting the charger) then cold storing.
But of course, this is all just general information. Always read the data sheet for your battery battery, otherwise call the company. You'd be surprised how informative some customer service representatives are, otherwise if they don't sound confident ask to speak with the technical staff.
Conclusion: you're safe enough storing your lead acids outside in a cold shed/garage/basement, the lithium's you must check the data sheet for coldest recommended temperature. Just make sure they have a decent charge on them before putting them there.
Note: 40-60% for LiFePO4 isn't mandatory but recommended by most manufacturers for getting that extra little bit of prolonged life. Although, do keep in mind that lower quality ones will swell/puff a bit (although still fully functional) if stored at a full charge for a prolonged time. The swelling typically resides after re-initiating regular use, but not always, hence the precaution.
