what are the maximum number of hydrogen bonds formed by a water molecule in ice?

the two hydrogens of the water molecule can form hydrogen bonds with other oxygens in ice, and the two lone pair of electrons on oxygen of the water molecule can attract other hydrogens in ice. Hence, 4 possible hydrogen bonds.

For temp greater than 4 degrees Celsius, it is 2.

for 0-4 degrees Celsius the transition state exists i.e between 2 and 4, accounting for the anomalous behavior of water.

For ice, it is four. the two hydrogen bonds form H-bond with the same O atom of another molecule in one of the directions and the O atom of this molecule forms H-bond with 2 H atoms of another adjacent molecule on the opposite side.

On the whole it forms a square network and there are vacant spaces within these squares accounting for low density of ice than water.

In water the molecules have kinetic energy and are in constant motion. Ice forms highly organized crystals due to their electrostatic charges, and loss of kinetic energy, and soon have fairly strong bonds. Which lets you go ice skating on a frozen lake.