Q.Will My Red Robin Die After A Cold Winter?
It has a lot of brown leaves.

Certified GKH Gardening Expert
Red Tip Photinia can withstand temperatures down to -12 degrees C (10 F). So if you had sustained temperatures below that, it may not have survived. You can scratch off some of the stem and see if it is still green underneath. If so, they should come back. Once you are past any more freezes, you can prune off the damaged areas.
https://www.gardeningknowhow.com/ornamental/shrubs/photinia/growing-red-tip-photinia.htm
https://www.gardeningknowhow.com/plant-problems/environmental/tips-for-saving-cold-damaged-plants.htm