Is it permissible to combine Fajr prayer with another prayer, or to perform tayammum instead of ghusl after marital relations at night due to the cold weather, even if it is possible to heat the water?

It is not permissible to abandon ghusl (ritual bathing) and tayammum (dry ablution) when one is able to heat water. Nor is it permissible to combine the Fajr prayer with any other prayer. All of this constitutes grave sins, as it leads to the squandering of prayer, and squandering prayer is a major sin.