The visitors started the brightest and Lloyd Owusu and Nicholas Shorey threatened early on, but it was the Cheshire side who took the lead in the 12th minute when Varney put a cross in from the left of the box.
Ivar Ingimarsson made a hash of his clearance and the ball deflected off one of his team-mates back into Varney's path and the striker unleashed a well-placed drive into the top corner of the net.
Vareny could have had a second five minutes later when his captain Kenny Lunt threaded a path inside Graeme Murty and gave him a run in on goal, but his effort rose over the crossbar.
Crewe were good value for the lead at this stage, but Reading fought back and left-winger Paul Brooker got free to pull the ball back across the six-yard box where leading scorer Kitson connected with a firm effort which Ince did well to hold at the second attempt.
The snow then fell during the half-time interval affected proceedings and the second half degenerated into a scrappy effort with Reading edging gradually back into the game.
Ince again needed two attempts to clutch hold of James Harper's fierce 25-yarder. The Trinidad & Tobago international was beaten by Ingimarsson's header when he came way of his line when he tried to punch Murphy's free-kick.
The ball bounced around Crewe's six-yard box and Kitson, in his second game, back after a long injury lay-off, bundled the ball through the keeper's leg for the eqauliser.
After that both sides stepped up the tempo to try and clinch the three points. Neil Sorvel's low shot forced Marcus Hahnemann into a save. David Vaughan's drive from outside the box caught the keeper out, with Varney hitting the rebound into the sidenetting.
Brooker drove just over at the end of a spell of Reading pressure in the dying minutes, but the draw will please neither side as Crewe have failed to claim a win in eight games, while the visitors' last win came on Boxing Day.