When I take off my glasses outside, my eyes start to burn. Is this normal?

Dry eye. Your glasses provide a protective barrier between the environment (wind, heat, dust, etc). When you take them off, these issue can cause your eyes to dry eye out and start to burn.
Dry eyes. Yes. Eye glasses do help shield the eyes from wind, dust, and sunlight. Also the rate at which your tears on the surface of your eyes evaporates is accelerated with air movement, which makes your eyes burn and tear.
No. Due to dry eyes. Exposure to wind and extreme temperatures can accelerate tear evaporation. Part of having dry eye syndrome is the inability for the eyes to respond normally to these types of stress. Try using artificial tears or see your eye doctor about other treatments, such as prescription medications to turn on tear production. Fish oil and oral sources of omega-3 are also helpful for burning dry eyes.