Reference: Fataawa Ramadhaan – Volume 2, Page 523, Fatwa No.489
Fataawa Ibn ‘Uthaymeen – Volume 1, Pages 505-506
Question: [What is the ruling regarding] the fasting person travelling from his country which is hot to a country which is cold or to a country where the day is short?
Response: There is no harm in that if he is able to do so, because this action is from that which reduces the effects of hardship of worship upon him, and doing that is something recommended.
And the Prophet ﷺ used to pour water over his head due to thirst and heat whilst fasting.
And Ibn ‘Umar (radhi-yAllaahu ‘anhumaa) would soak his garment [he was wearing with water] whilst fasting.
And it is mentioned about Anas ibn Maalik (radhi-yAllaahu ‘anhu) that he had a trough of water which he would get in whilst fasting.
[And] all of this [was done] in order to reduce the effects of hardship of worship; The more an act of worship is made easier upon a person, the more active he will be in doing it whilst he is at peace and ease.
It is because of this that the Prophet ﷺ prohibited a person praying whilst he has the urge to urinate, as he ﷺ said:
[And] all of this in order for a person to carry out [his act of] worship at peace and ease whilst facing his Lord.
And based upon [all] this, there is no harm in the fasting person remaining in a cold air conditioned room or that which is similar.