Reindeer.

junk I've been wondering about reindeer. As domestic animals, they make sense only in arctic regions where other animals do not thrive.

John Croft writes:

Could these Indo-iranian loan words have come into Finno-Saami with the introduction of Reindeer herding from across the Urals a fair while after the contact with Balts and Germans. Certainly reindeer herding is supposedly adopted first by Samoyeds in contact with Indo-iranians, who coppied their use of the horse. This spread of technology could probably spread Iranian loan words that could have entered Samoyed languages, especially if associated with reindeer herding technology.

From the National Park Service:
In Eurasia people long ago began to tame wild caribou. Some anthropological studies suggest that this occurred in the southern Altai mountain region about 5,000 years ago.
http://www.n ps.gov/bela/html/rangifer.htm

I cannot vouch for the accuracy of the National Park Service's statement, but for the sake of argument will take it at face value. This is the only reputable site that gives a date for the domestication of reindeer.
The Altai Mountains define the northwestern and southwestern borders of Mongolia. The Altai mountains proper contain headwaters of elements the Ob, Yenisey (principally), and elements of the Lena river systems. The NPS may actually be referring to the Mongolian or Gobi Altai ranges, which define the southwestern border of Mongolia, with Xinjiang.
With the date of domestication for Rangifer tarandus set at 3000 BCE in the 'Southern Altai Mountains', we are probably in post-PIE times. This part of the world was occupied by the Afanasevo culture, 3500-2500 BCE, and is imputed by many to be proto-Tocharian. The Afanasevo culture, however, contains remains of cattle, ovicaprids, and horse -- all of which do not suggest a reindeer-domesticating culture to me.
In any event, I would not look for reindeer in northwestern Europe until well after the breakup of PIE. I do wonder if Uralic-speakers can be associated with their domestication; such a question is of course unanswerable.
If 3000 BCE is the correct date, and the Southern Altai the correct place, and considering the evidence from the Afanasevo culture, we have rather hard evidence for early east-west movement. There is a possible hint that the origin of Uralic just might be further east than is usually stated.
Considering the poverty of my resources to investigate the question, my conclusions are only speculative. I suspect most of the really good data is buried in Finno-Scandic publications.
Mark.