The promotion-chasing Robins came closest to a winning goal but Edgar Davids' Bees held firm and earned a share of the points at Underhill.
The closest either side came to a breakthrough was shortly after half-time when Cheltenham midfielder Kaid Mohamed's shot struck a post following clever play from Jermaine McGlashan.
In difficult conditions caused by heavy snowfall, there was little action of note in the first half with neither side able to take control of the game.
Home striker Jon Nurse forced a save from Scott Brown in the 20th minute, while at the other end Paul Benson and Russell Penn fired off target.
After Mohamed hit the post, Brown kept out Mark Byrne's deflected hit while Bees stopper Graham Stack saved from Sam Deering.
The closest Barnet came was through midfielder John Oster's long-range effort that went just wide.