Allah the Almighty commands:
“Those are the ones to whom We gave the Book, and judgment and prophethood. If these ones ignore it, We will delegate other people who will not ignore it. Those are the ones that Allah accepted to the right path. Follow then, their path, and say: I ask of you no reward, it is merely a true information to all mankind.” (6:89-90)
As the command of this verse, the Messenger of Allah followed the path of Jews and Christians on issues where there is no new command from Quran or until a new command has been revealed to him.
Regarding your question,
The Messenger of Allah had once forbidden using perfumes while dressed in ihram. A narration is like this:
“It is asked to the Messenger of Allah: What do you say to a man who puts on perfume before getting dressed in ihram? He answered: Clean the smell you put on your body three times.” (Bukhari, Hajj/Pilgrimage 17; also Muslim)
Most of the scholars disapprove using perfumes according to this narration.
However, we also have other narrations from the last hajj of the Prophet. Aisha reported:
“I used to put the best perfume on the Messenger of Allah before he got dressed in ihram.” (Bukhari, Hajj/Pilgrimage 7, Libas/Clothing 79-81; also Muslim, Tirmidhi and Darimi)
“I almost see the glitters of musk in his hair while the Messenger of Allah was reciting talbiyah.” (Muslim, Hajj/Pilgrimage 39)
“The Messenger of Allah used to put the best perfume before getting dressed in ihram. I used to see the glitters of it in his hair.” (Bukhari, Hajj/Pilgrimage 144)
These last narrations show that the judgment on this issue was changed and that the Messenger himself was using perfume before getting dressed in ihram. So there seems no problem to put on perfumes before getting dressed in ihram. However, we don’t have any evidence for after getting dressed. So, it would not be permissible to use perfumes (also cologne, etc.) after getting dressed in ihram.
Resource: Abdullah Trabzon, Hac İbadetinde Yasak Davranışlar (Forbidden Acts During Pilgrimage), PhD Thesis, Istanbul University Institute of Social Sciences, 2008, p.122-124.