Let's say you live at a moderate (temperate, in today's terms) latitude during the last glacial maximum. You're probably in some kind of steppe or taiga biome, even though you're at 40 degrees north, and you've never known hot weather. If you're outside on a sunny summer day, would you still get a suntan/sunburn like you would in today's climate? Aside from temperature, which doesn't cause sunburn, would there be any relevant atmospheric differences that might affect the UV radiation?
Yes, of course, the suntan/sunburn depends on the overall energy in UV radiation coming from the Sun to one's skin and this quantity is virtually unchanged in the glaciation cycles, at least if you average it over seasons. What primarily matters is the angle between the Sun rays and the plane of the skin; and the angle between the Sun rays and the plane of the Earth's surface (because it determines the thickness of the atmosphere that diminishes the UV radiation as the Sun rays have to get through).
The glaciation cycles (lasting 20,000-100,000 years and occurring in a recent 1 million years or so) are caused by the Milankovitch cycles, subtle irregularities in the orbital motion of the Earth: the eccentricity, axial tilt, and precession matter. Those variations affect the average amount of sunlight near the Arctic Circle in the summer – which is the crucial place and season because there's a lot of potential for ice sheets to grow there or recede and this growth or disappearance of Arctic ice sheets gets exported to other places of the globe.
However, the variations of the sunlight in the moderate zones are very small.
It's not such a speculative thing. You may easily get a suntan/sunburn in the cold winter (in a moderate climate), too. It's less usual because people are usually well dressed in the winter. Still, the face is often unprotected and skiers know that they must be careful.
Assuming it's a cloudless day, then yes you will get a sunburn just as you would today. Sunburn is caused by the intensity of ultraviolet light, and this didn't change (much) during the ice age. The external temperature makes no difference: it's just the uv intensity that matters. Any skier can tell you that :-)
Actually, now I think about it, it's possible the amount of ozone might have been affected by whatever changes triggered the ice age, and if the ozone levels changed this would change the amount of uv hitting the Earth. However I suspect this would be a minor effect and my initial conclusion still applies.