Current distribution for parallel zeners
Low voltage Zener diodes (about 5V) feature true Zener breakdown, i.e. band-to-band tunneling. The larger the temperature, the more likely the tunneling occurs because the larger the carrier energy (and the smaller also the energy gap).
Therefore, there could be a thermal run-away. In fact, unlike normal diodes (or LED diodes) in forward conduction, small mismatches can lead to large current variations as the curve is very steep in breakdown voltage. The Zener carrying more current will likely heat more (Which will decrease the Zener voltage etc.).
High-voltage Zener diodes (e.g. 10V or more), instead, feature avalanche breakdown. The carriers are accelerated by an electric field, and if they reach enough energy, they will produce more electron-hole pairs, due to impact ionization (which are in turn accelerated by the electric field, etc.). However, the larger the temperature, the larger the lattice vibration and thus the smaller the probability that an electron can gain enough energy between impacts, therefore the less likely they can ionize (i.e. produce another electron-hole pair).
In this way, there will be a negative feedback, that will make the diode initially carrying more current to be less conductive (therefore the current will spread more equally).
The datasheets shows in fact different temperature coefficient for different Zener values.