There is a well-known midrash that says (my translation):
Q: How do we know that Yaakov wore a shtreimel?
A: It says: "And Yaakov left Be'er Sheva". What, he left without a shtreimel?
However, an ancient manuscript of the midrash (MS Hamanovich 82) contains this version (my summary and translation):
Q: How do we know that Yaakov wore a kippah?
A: It says: "And Yaakov left Be'er Sheva". What, he left without a kippah?
It seems to me that both cannot be correct. The contradiction cannot simply be explained by saying that under the shtreimel he had a kippah, because how are we to know if he had a kippah under the shtreimel if all we see is the shtreimel? On the other hand, MS Hamanovich utterly ignores the existence of the shtreimel and focuses on the kippah. In terms of the issue of walking around bare-headed, all that is necessary is some form of head-covering. That MS seems to focus on whether or not he had any sort of head-covering at all, and comes to answer that.
So, therefore, my question is: In light of MS Hamanovich 82, is there any way to know whether or not Yaakov had a shtreimel?