The equator during an ice age is unlikely to be where the equator is located during mild periods, such as the one we are currently experiencing. This is especially true if our planet is hollow. However, we do not have to accept the hollow Earth hypothesis to come to the conclusion that the location of true north, and hence the location of the equator is different during ice ages than when Earth is relatively ice free.
The physics for this is simple. A spinning body must have a balanced distribution of mass, otherwise it will wobble catastrophically until a balanced distribution is found. Either way, it will always seek to find a balanced distribution. The orientation of true north and the location of the equator today are therefore reflections of a balanced distribution of mass.
However, during the last ice age, the enormous ice sheet covering the northern regions of our planets were not distributed equally across what we have as true north today. The center of the ice mass was located at Hudson Bay in Canada. True north must therefore have been somewhere between current true north and Hudson Bay. The equator must for the same reason have been skewed farther up in places like Siberia, and farther down in places like Peru.
As it happens, we have some interesting evidence in support of this. The magnetic north pole has been located close to Hudson Bay for most of modern history, suggesting that this may have been true north at some point. Siberia was ice free during the last ice age, suggesting that it may have been located closer to the equator.
Another striking observation is that the biggest, most sophisticated megalithic sites are located close to a great circle that cuts through both Egypt and Peru. This great circle may very well have been the equator at the time. With ice covering large parts of the globe, it is natural to expect human settlements at the time to have been clustered around the equator. It is therefore very telling that these settlements clustered around a great circle that is askew from the equator we have today.
What’s more, some of the most ancient monuments known to us are oriented along this same line. The people building these monuments were very much aware of it, much like we are aware of the east-west axis we have today. We like to orient monuments like churches along the east-west axis. The same was almost certainly true for early humans.
This again gives us a way of dating ancient monuments. Those that are clearly oriented along the current east-west axis are post ice age. Those that have a clear orientation parallel to the ice age equator are from the ice age.