I wore this hat on a blustery winter day in Quebec while on the cross-country ski trails.  It was absolutely perfect - I'm so glad I made the purchase.  The pursuit hat has a lower profile--to fit my smaller head--better than the alpine hats (I did not buy it for use under a helmet).  It does not have the warmth of the alpine hat (which is too warm for me for skiing), but it does have more warmth than the running hats.  I did not find it to be too tight as some reviews stated.  The headbands suffice for me on warmer skiing days, so I found the pursuit hat to be perfect on my cold skiing days.