It is 99% likely that GSN will air a Steve Harvey Family Feud marathon on New Years' Eve (Thursday, December 31st) or New Years' Day (Friday, January 1st). This is due to the fact that GSN will air John O'Hurley Family Feud in the 12pm ET hour weekdays next week (12/21-12/25) and the following week (12/28-1/1). Although we do not have the advanced schedule yet for the week of December 28th, GSN said in their cover email from the December 21st schedule that John O'Hurley Family Feud will air at 12pm and 12:30pm ET for two weeks only.
Family Feud restrictions for GSN
A 'Feud cap' has been placed on Steve Harvey Family Feud, where there can only be a limited (but not too limited, obviously) number of Steve Harvey Family Feud airings per week. There are also restrictions in the 8pm ET hour weekdays. There is another restriction that GSN cannot air the 2012-13 or 2013-14 seasons of Harvey Feud (the HD season) prior to 9pm ET weekdays, where the 2010-11 and 2011-12 seasons air at 12-1pm and 6-8pm ET (Harvey's first two seasons).
GSN recently renewed a lease to keep the 2010-11 and 2011-12 seasons of Family Feud on the schedule through the first quarter of 2018. GSN's contract is to get new seasons of Family Feud a year after they stop airing (or two years from launch). For example, the 2013-14 Family Feud season came around to GSN in September 2015. The 2014-15 season is expected in September 2016. GSN does not have the rights or any contract to seasons beyond 2014-15.