my mirrors, which are 1/4 inch float glass recycled from a hotel lobby ( for a grand total of $50) are mounted outside and have survived 10+ years of snow, rain, hail, wind, temps ranging from -10 to 110.
If you are outside, do not glue the mirrors- the plywood will absorb moisture and expand and ctronct and the glass will expand and contract with temperature- the two materials have different rates of expansion, so if glued, the mirrors may warp or crack.
Do NOT mount them with “mirror clips”- those are meant for residential , not sport use, and in weather, the screws loosen and come out of the pklywood and the mirrors will fall.
We have ours mounted on 3/4 inch plywood backing. There is a 2 x 4 frame around the plywood. The frame gets mounted, then the mirror is mounted inside the frame and 1 x 1 or 1 x 2 is applied, nailing carefully into the 2 x 4 frame with finishing nails to hold the 1 x 2 on. The mirror “floats” within the frame.
Liz Steacie, who sometimes posts on this board, originally had closet door mirrors mounted in her arena and they worked great. They come already mounted in frames and you can hang them from the the closet door track, fastened to the arena wall. Another inexpensive option, especially if you go to a house demo sale and can find them second hand!