Our expert, David Williams, has responded:
Use a good hand lens to check if the eggs are round or onion shaped (they will have a stalk coming from the top). If the eggs are round they probably belong to Bryobia mites. If the eggs are onion shaped they are most likely ERM (European Red Mite) eggs. Either way, these eggs are the overwintering stage of the mites.
If there are lots of eggs then you are likely to have an early infestation in spring because the eggs start to hatch around green tip. They are most susceptible to oil sprays applied as close to green tip as possible. Spraying mid-winter is mostly a waste of time.