Is it permissible to pray merely by repeating minor ablution (wudu') or is major ablution (ghusl) obligatory after involuntary urination due to the unavailability of water, especially in cold weather?

Whoever prays without ablution (Wudu') has an invalid prayer and must repeat it after performing the lawful ablution. He is not required to perform a full ritual bath (Ghusl) unless there is a reason necessitating it. You should have sought a way to perform ablution, even if it meant leaving your workplace. Indeed, one who is in cities usually does not lack the means [to perform Wudu']. However, if one is unable to use water due to a valid excuse, then tayammum (dry ablution) is permissible for him. As for purification from urine, it is sufficient to perform istijmar (cleaning with stones, tissues, or similar purifying objects) and water is not a condition for it.