It used to be that we would talk about not cutting alfalfa for 4 weeks before last killing frost. The reason was to allow alfalfa to build energy reserves in the roots going into winter. It seems that is not discussed much anymore. I think better alfalfa genetics - and crop nutrition - have lessened that risk.  

As far as I know, there is no restrictions on cutting alfalfa after a killing frost.  I think we have seen that a killing frost will cause leaf drop.  So, cutting soon after a killing frost will retain more leaves in the forage, compared to wait to cut.  That would be an incentive to cut, as opposed to wait - so more leaves are retain.