An army of volunteers worked through the morning to clear snow from the pitch to get the game on but it seemed they would regret that decision after a sluggish start by the hosts.
The Blades opened the scoring after just over a minute when Nick Blackman's inswinging corner was headed home by a towering Harry Maguire.
Jeff Hughes had a good chance to level for County on 11 minutes after poor defending from the Blades but he scooped his shot over.
The home side had a mountain to climb after 24 minutes when Francois Zoko was sent off, first receiving a booking from referee Mark Haywood for protesting a free-kick before seeing red as he continued his outburst.
However the away side never really pressed home their advantage and after 80 minutes Judge glanced home an Alan Sheehan free-kick to give the Magpies a point.