If you mean buzzcuts in the modern sense, no; at least not for the US Army. They absolutely, however, had grooming standards; its a basic tenet of military hygiene. Hair had to be short at the sides and back; away from the collars and not covering the ears. Haircuts happened when they could and the frequency of them were never guaranteed. However, especially in the US, battalions could rotate off the line with frequency at the end of a drive or series of attacks; so obviously it isn't a case of 'hair growing back.' One has to remember that 'being at the front' doesn't mean you're constantly dodging bullets; it could mean your Battalion is in division reserve, or that you're in a low-activity area; lulls happened even in the high tempo operations of WWII.

The idea of 'high tops' in hairstyles isn't out of the ordinary across any armies of WWII; the general rule of 'short sides, above the collar in the back' generally applies to every branch and army, with obvious variations.

Finally, and as always, lets never forget that Band of Brothers is an interpretation of a book made for our entertainment; and such content will always have inconsistencies, as myself and /u/rittermeister have discussed before.