Former Nottingham Forest manager Hart and ex-Peterborough United boss Halsall have stepped in on a temporary basis after County parted company with Shaun Derry and his assistant Greg Abbott on Monday.
It remains to be seen how long acting academy manager Hart and head of academy coaching Halsall will lead the club, but the former is the bookmakers' favourite to land the job on a permanent basis.
Alexander made over 400 appearances for Preston in two spells at the club, but will be attempting to put a spanner in the works in his former club's bid to secure automatic promotion.
Second-placed Preston are unbeaten in 10 league matches and hold a three-point lead over Swindon Town, who occupy third spot, while Fleetwood are still in the hunt for a play-off spot.
Leaders Bristol City lifted the Football League trophy last weekend and hold a 10-point lead at the top of the table ahead of a home clash with play-off hopefuls Barnsley, managed by former City midfielder Lee Johnson.
Swindon and Preston have a game in hand on Steve Cotterill's men and the former will attempt to secure a fourth successive win when they host MK Dons on Saturday.
Dean Saunders' resurgent Crawley Town side will be eyeing a fourth win in a row at home to Gillingham, Bradford City face Oldham Athletic and Chesterfield take on Walsall.
