Before you can decide on a power source, you need to know how much power you need (Watts W), for how long (Watt-hours Wh).
If the coop is open-cage, it's going to need a LOT of power to make enough heat for those 20-30 degree daytime temperatures to keep them up to "room temperature", and way more heat for the nighttime temperatures that must be even colder.
If the coop is closed-up, like a shed or barn style, it'll take a lot less heat, but it'll need to be well-sealed against air leaks especially if there is any breeze, and if it's windy especially.
So, what equipment do you have right now that you use, for how many hours in the daytime?
Then, what equipment do you have right now that you use, for how many hours in the nighttime?
What extra equipment you do you have right now that you use for extra cold times?
Knowing hte power requirements for these will help us help you figure out how big an alternate power source you will need, and how many Wh of storage you need for the times the alternate source is not available, worst case.
For instance, if there is a stormy week that you don't get any sun, or not enough, the storage battery would have to be able to supply the entire power needs for the entire time until the sun is available again.
Additionally, the solar systme would need to be able to not only supply the entire power needs for the system while it is generating, under worst-case daylight conditions that the solar could still operate under, it would *also* have to be able to supply enough power at the same time to fully recharge the storage system, so that it can run the equipment at night, and be ready to run the system for however long the whole system needs to run worst case (like the stormy week instance).
If the "off grid" is an *optional* thing, where you *can* run power out to the coop in an emergency (like the stormy week or whatever), then you don't need as big a battery--just big enough to run whenever the panels can't supply the load and charge the battery at the same time.
How large a budget do you have?