He had a wet dream but he did not do ghusl because it was very cold
Question

I was once sleeping in the afternoon after taking lunch. i had erotic dreams & sufferred from nocturnal ejactulation. when the adhan for assar was being given , i woke up. s it was very cold i could not take a bath. i washed the semen off from my pants, did taimyum and continued with my asaar prayers. did i do the right thing? is it necessary to take a bath after having a wet dream or is it suffficeient to wash off the semen & do wadoo to become clean.  
In fact in view of the cold i tokk bath only after a few days, & contined to perform salat all these days using the same garment. i hope i have put the problem before u lucidly
Praise be to Allah.It is the mercy of Allah towards His slaves that the obligation to do certain duties no longer applies when one is unable to do them, because Allah says (interpretation of the meaning): 
“Allah burdens not a person beyond his scope” [al-Baqarah 2:286]
This also includes not being able to do ghusl when one is junub (in a state of impurity following sexual activity); whoever is not able to do ghusl because he is sick or it is very cold may do tayammum instead and he does not have to repeat his prayers, because of the hadeeth of ‘Amr ibn al-‘Aas who said: “I had a wet dream on a cold night during the campaign of Dhaat al-Salaasil, and I was scared that if I did ghusl I might die. So I did tayammum and prayed, then in the morning my companions mentioned that to the Prophet (peace and blessings of Allah be upon him). He said, ‘O ‘Amr, you led your companions in prayer when you were junub.’ I told him what had kept me from doing ghusl and I said, ‘I heard that Allah says (interpretation of the meaning): “And do not kill yourselves. Surely, Allah is Most Merciful to you” [al-Nisa’ 4:29].’ The Messenger of Allah (peace and blessings of Allah be upon him) smiled and did not say anything.”
(Narrated by Abu Dawood, 334; classed as saheeh by al-Albaani in Saheeh Abi Dawood, 323; al-Bukhari narrated it as a mu’allaq report). 
If you were in a place where you could not find any means of heating the water and you feared that you might become sick if you did ghusl with cold water, then what you did was correct and you do not have to repeat it.