If one gets into a state of Janabat due to discharge of sperm while talking to his wife during early hours of day when there is plenty of time till Nimaz Zohar and lives in a cold climate where taking bath with cold water is very difficult. In this situation, if he goes for urination and makes taharat. When the time of namaz approaches, can he offer the wajib prayer with just doing wudhu and not doing the ghusl janabat? will his prayer will be valid or void?

Wudhu is not sufficient, ghusl is wajib
If one can not do the ghusl due to sickness or use of water is harmful then has to do the tayammum.