The 18-year-old has only recently returned to United following another loan stint, having made a handful of appearances for Vanarama National League North outfit Darlington after linking up with the Quakers in September.
Woolston could make his Spartans debut against Barwell today, Alun Armstrong's side currently second in the standings behind Whitby Town.
Capped by England at Under-17 level, Woolston also spent a month on loan with National League side Gateshead last season.