Do Arctic foxes live in burrows?

Answer 1

Yes, here is more helpful information:

Minks are found in the forested areas of North America, Europe, and Siberia. Mink are widespread in Britain's mainland, except in the mountainous regions of Scotland, Wales and the Lake District. They are also found in the Isles of Arran and Lewis. In Ireland they are less common.

The American mink (Mustela vison) is found in places which suit its habits throughout almost all North America, from Florida to the Arctic, except in arid parts of the southwestern U.S. They can be found in wooded areas and fields near streams and lakes. They do not dig burrows, but instead take over dens abandoned by other animals.

Waterside habits

Minks like to live near water and are seldom found far from riverbanks, lakes and marshes. They can live in riparian areas, which is common. Even when roaming, they tend to follow streams and ditches. Sometimes they leave the water altogether for a few hundred meters, especially when looking for rabbits, one of their favorite foods. In some places, particularly in Scotland and in Iceland, where they have become a problem, they live along the seashore. Sometimes they live in towns, if suitable water is available.

If something like a large weasel or small otter is seen, near a lake or a river, or on the sea shore, it may well be a mink. Unlike the otter, which is only active at night when there is no danger of human disturbance, the mink is about at all hours, even when people are in evidence.

It is difficult to estimate the number of mink in Britain today. A mink needs several miles of waterside to make its home and, considering the thousands of miles of waterways and courses throughout Britain, there could be thousands of mink in Britain.

Source: Wikipedia

Answer 2

In the wild they do.