Andriy Yarmolenko put the visitors in front on the stroke of halftime but a penalty by Ivan Krstanovic deep into stoppage time at the end of the game earned Zagreb a point.
Zagreb finished bottom of the group with one point from six games, four points adrift of Kiev who qualified for the Europa League in third spot.
Paris Saint-Germain (15 points) and Porto (13) went through to the last 16 of the Champions League after the French side defeated the 2004 winners 2-1 at the Parc des Princes.
The blizzard caused Bulgarian referee Stanislav Todorov to lead the players off the pitch in the Croatian capital after 10 minutes.
The game was delayed for 17 minutes while groundstaff painted the lines on the pitch red.
Snow continued to fall on the resumption but conditions were farcical with players repeatedly sliding to the ground as they tried in vain to catch up their opponents.
The ball kept getting stuck in the snow and back passes to the goalkeepers were fraught with danger.
Zagreb were nonetheless determined to avoid equalling Anderlecht's record of 12 successive defeats in the competition with Fatos Beqiraj, Duje Cop and Sammir all looking lively in attack.
It was Kiev, however, who took the lead when midfielder Yarmolenko struck with an improvised volley from outside the penalty box that bounced off the crossbar to beat keeper Ivan Kelava.
Zagreb threw everything into attack in the second period and were finally rewarded when keeper Maxym Koval upended Krstanovic and the substitute converted the penalty to spark celebrations among his team-mates at the final whistle.
