Simple (Wrong) Analysis
Assuming the coefficient of friction on the ice is approximately the same for the tires and shoes. It would do just as much good to get into the plane as to try to push it. Both would increase the frictional force by at most $\mu\,m\,g$ Having established an upper bound for the effectiveness of pushing we can compare this to the magnitudes of the forces already in place.
An empty 737 has a mass around 30,000 kg. A human on the larger side has a mass around 100 kg.
So the human pushing on the plane could increase it's resistance to sliding by about 0.3%.
Considering wind generally comes in gusts that vary by more than 0.3%, the plane would still slide during the gusts, though in theory slightly less than it otherwise would have slid.
Suppose ice cleats were available. Now the human's force to resist movement is not limited by friction but by strength. Unfortunately, the human squat record is for a force less than 6 KN. The coefficient of friction between rubber and ice is around 0.2 so the plane was already dealing with 60 KN of force. So in this case the human could increase the resistance to sliding by no more than 10%, this may be close to the variation in wind in non-extreme weather situations, and might have actually helped. However, it would have been extremely dangerous, and likely could have only helped for a very very limited time.
It it were me, I'd just shove the ice cleat under the tire and be done with it.
A more complicated Analysis
Having watched the video it appears that the aircraft is rotating rather than sliding sideways. This is important as it seems the rear tires are keeping traction and only the front tire is slipping. Thinking about the weight distribution of an aircraft, most of the weight is on the rear tires. In fact, for a 737 the front wheel weight seems to be around 15 KN, so using the 0.2 coefficient of friction that's only 3KN of friction. It seems that not only could a cleated (very strong) human help out, but could in fact push the plane back into place. Someone in just shoes could still help out to the tune of around 5-10% which could be significant. Note though it would be most effective to push near the nose as that would give the longest lever arm to give the most torque.