I've heard about the Greenland Viking culture disappearing due to a cooling climate making their source of sustenance no longer viable, while the Inuit were able to keep hunting and fishing like they had before.
Did the Vikings simply die out and/or leave, or did a significant number of them join the Inuit?
In short answer: to join in the Inuit especially in large number is the least presumable alternatives of the three that OP listed (to die out simply, to leave, and to join in).
It is true that an early modern Icelandic author suggests the possibility before the "re-discovery" of Greenland in the 18th century, but none of the (near contemporary) written, archaeological, and genetic evidence as well support this hypothesis.
As I summarized some basic premises before in: Did the Vikings ever mix with the Inuit that lived in Greenland?, experts on the relevant field of research (archaeologists, ethnologists, and historians) have not reached an consensus on what exact characteristics of the relationship between the Norse and the non-Norse arctic people(s) in the later phase of medieval Norse settlements (13th to the early 15th centuries) were like, or what of those between the old and the new non-Norse arctic peoples, namely late Dorset culture and Thule culture (direct ancestor of the current Inuits).
AFAIK the latest genetic research on the sample of the current Greenlanders, published around 2015, does not show any trace of possible incursions of genes of medieval Norse into the Thule culture people, nor even those of Late Dorset people into the Thule people (Moltke et al. 2015). It probably means that the relationship among the Thule culture people and the other two former occupants of medieval (in European timeline) Greenland was not so close.
On the other hand, while most of the scholarship, regardless of their discipline, agree that the climate certainly played an important role in the fate of medieval Norse Greenlandic settlements, how it was really crucial in the 14th century and to what extent the Norse people couldn't cope with its challenge, can also be debated - In contrast to the famous popular history picture formulated by Jared Diamond's Collapse, grave archaeology has lowered the maximum total population of the Norse settlers from 5,000-6,000 to 2,000-2,300 (around 1300), so the environmental burdens of the Norse settlers like the soil erosion might have not so serious than generally assumed.
As for written evidence on the possible relationship between the Norse settlers and the "Skraelings" in the former's last phase, it might also be interesting to check my previous posts in: Multiple Questions Regarding the Thule Culture.
Reference (as for more, please check the linked post):