That's exactly what I used to insulate my coop. I used plywood on the inside to cover the styrofoam so the chickens wouldn't peck at it. I got all my styrofoam for free too , so it was really cost effective.
I, too, used sheet styrofoam as insulation........between the 2 x 4s, all the walls and ceiling.
I then ordered 4 x 8ft panels of 1/4inch white plastic.........and covered the styrofoam with that.
The plastic panels are awesome for keeping things clean.....they wash down easily.....and make everything bright inside the coop!
The 'only' drawback to the styrofoam is it is SOOOOOOOOOOOO messy when cut! Little white beads of it.....
EVERYWHERE!!! But a broom and shop-vac took care of that when all when all the cutting and installing were done.
And styrofoam is cheap!!! (Other types of insulation? Not so much!!)
As I have mentioned on several other of your threads, styrofoam is good insulation between plywood walls. Just go around to stores and see if they have any from shipments of merchandise that they'd let you have -- you will have to stop and ask *often* b/c it's totally random what they have on any given day. I've gotten excellent stuff from the Liquidation World that used to be in Uxbridge but that won't help you as it is now closed; you might try Dollaramas, I've gotten some there too, but really just go ask around at a bunch of big stores.
If you are all that concerned about cold, I would really suggest building your walls with 2x6 instead of 2x4 studs and filling all the extra thickness with insulation... that will nearly double the R value of your walls and really helps retain heat.
You don't need to put all the insulation in at once. You can tack the inside wall on with screws til you accumulate enough insulation to fully fill it; or just leave the inner plywood off until you can insulate. You'd want all 4 walls plus the ceiling done by winter of course but it means you don't have to necessarily have all your insulation material before putting chickens in the coop.