In difficult conditions due to the falling snow, neither side were able to break the deadlock but the 0-0 scoreline was viewed positively Yates.
The visitors went closest to winning it as Kaid Mohamed crashed a shot against a post after good work by Jermaine McGlashan shortly after the break.
Barnet's best moment fell to midfielder John Oster but he fired just wide of Scott Brown's goal.
Cheltenham fell to fifth in the table but moved a point closer to the top three, pleasing Yates.
He said: "I'm proud and pleased we haven't got beaten as this is a tough place to come and the conditions were difficult as well for both sides.
"We wanted to give our strikers a little bit more to work with and we did that in the last 20 minutes. I wanted us to make space in behind them and use the wings, and we did that for most of the game. We couldn't quite finish it off and as the game went on we got a bit bogged down with the pitch.
"We had to make a few changes as the game went on and that gave us a bit more of a threat in the wide areas.
"I felt a bit for the boys and the paying supporters as well because even though that could be an important point for us, it wasn't the most entertaining game to watch because of the weather and conditions."