1966-67 would probably be on the extreme end of what one can expect- that was one amazing book end winter that won out by its sheer duration and became historic- somewhat like 2014-15? 1966-67 stands out compared to other book end winters because we actually got a major snowstorm down here in December, before the mild pattern ensued. I was compiling a list of winters that seem to match what you're looking for, with varying lengths of mild periods book ended by cold on either side to varying degrees, that I've experienced. Here are the ones that snapped back to cold:
1989-90 (very briefly and very late, in early April, with snow!)
1996-97 (mostly in New England, big bookend winter in Worcester and interior Mass., the April snowstorm was a mild bust down here.)
1997-98 a renegade snowstorm as winter was ending
2005-06 and 2006-07 I already discussed these in an earlier post
2014-15 I hesitate to even include this because the snap back to snow and cold was SO extreme and lasted so long, somewhat like 1966-67.
2015-16 almost as extreme as 1966-67 but the warmth came in earlier (December) and so did the cold- we had a 30" + snowstorm on Jan 20th and below zero lows for Valentine's Day! JFK became only the second location (besides Norfolk, VA) to experience a 40" snowfall season with an average winter temp above 40F!
The last three winters were also somewhat bookend winters (2016-17, 2017-18 and 2018-19). The first two were more extreme than the last one.
*the number of book end winters seems to be on the increase, perhaps due to the abnormal warming in the Pacific and Indian Oceans?