The daily water needs of the reindeer will increase when on supplementary feeding. Winters with low snow and rainfall often cause problems with bad hygiene in paddocks and lack of clean snow for water access. Reindeer are fine eating snow, given that the snow is clean, but the best solution is to have access to running water within the enclosure.
If there is a shortage of clean snow within the enclosure, more enclosures are needed, the size of the enclosure might have to be increased or supplementary feeding could be done outside the fenced area. Another possible solution would be to shovel large amounts of clean snow into the enclosure.
Heated water buckets or water cribs could be an alternative if you have access to electricity. The cribs need to be cleaned out on a regular basis and the water needs to be cool to prevent bacterial growth.
A cold stream through the paddock could serve as a good alternative, but the cold source needs to be kept open and prevented from freezing and accessible to the reindeer. Water must be kept running and the outflow unobstructed. Feeding points should never be placed upstream since this will contaminate the water.
A brief shift to mild weather in late winter/early spring can quickly result in compromised hygiene and dirty water. Suggested measures are to quickly expand the enclosure, change enclosure or release the reindeer out on pasture in order to offer a new source of water.