Well yeah, colder less desirable climate for growing would have an adverse affect on growing migration to those regions. But climate was probably not the motivation for migration. Even today people migrate for climate reasons, in addition to other reasons. Seems like a really lame study to me.
They discovered migration started quickly out of south-eastern Europe, with Neolithic farmers pushing out the existing hunter-gatherer population. This was demonstrated by how little the DNA of the two groups mixed. As they moved north, the climate became less suitable for the crops they had bought with them. Their pace of movement slowed, changing how they interacted with local hunter-gatherers, which can be seen through increased genetic admixture of the two groups...
Yeah, lame, sounds like it was really easy research as well.