I run mine year around. I've lost two cameras (Moultrie) due to weather, and stopped using that system (to be fair, it was the older Moultrie Mobile system, not the current one).
I had to replace the battery box on one Cuddeback (J-version). The Cuddeback's have been out three to four years, I have several SpyPoints that have been out two plus years.
While the batteries go dead due to snow accumulation on the cameras, but they tend to recharge in good sunlight. Occasionally I have had to bring a camera in to charge the battery (more common on the StealthCams).
I do an annual "replace/charge/check/clean each spring" for all cameras.
Rationale: I like to get data year round, plus it provides some level of security on the property. Knowing what predators, deer and general conditions on the property are a plus.