Did people ski during the ice age?

Actually, it is theorized they may have. The Sami people of Scandinavia were known to ski for a number of different reasons including hunting and warfare as recently as 5,000 years ago, and skiing may date back even further.

The problem here is that the term "ice age" is a bit generic. There have been five major ice ages identified in Earth's past:

1. The Huronian glaciation or Makganyene glaciation - 2.4 to 2.1 billion years ago
2. The Cryogenian glaciation - 850 to 630 million years ago
3. The minor the Andean-Saharan glaciation - 460 to 420 million years ago
4. The Karoo Ice Age - 360 to 260 million years ago
5. The Pliocene-Quaternary glaciation - started about 2.58 million years ago and continues today with cycles of glaciation and retreat interrupted by interglacial periods.

The last commonly accepted glacial period of the current ice age ended about 10,000 years ago, but the current interglacial retreat continues.

So, technically, any activity involving Homo sapiens sapiens that has occurred in the past 200,000 years of the past 2.58 million years has actually taken place during an ice age.