Yes after fajr n asr salah nafl are makrooh , but brothers n sisters there are exceptions.
Like the one brother rashad mentioned is not permitted , coz it is a voluntairy nafl act.
But there are exceptions to pray at the time after asr n fajr , for example
The 2 rakats performed after dong the tawaf of the kaaba , for the one doing umrah or for nafl tawaf , u gotta pray them n you can pray them even if its time after asr or fajr , n as u see people get to the haram at diffrent times n tawaf is always going on so this is an exception and one has to pray them even if its makrooh time
Second nawafil like Tahiyatul masjid n tahiyatul wudoo
coz the prophet sala lahu alihi wa sallam said , when u enter the masjid DO NOT SIT untill u pray 2 rakats, so this hadeeth many people of knowledge take as WOJOUB of tahiyatul masjid as the Prophet sala lahu alihi wa sallam has ordered NOT to sit untill u pray 2 rakats , so if one goes to masjid after asr he can pray these 2 rakats n InshahAllah his actions is alright. As for tahiatul wudho than that is only for a person who is used to do it , i mean who always prays 2 rakats after he makes wudhoo , this person if made a wudhoo after asr or anyother makrooh time he can pray the 2 rakats InshahAllah.
Third Sunnah of fajr : It was proved from the famous hadith that a companion prayed 2 rakats after fajr salah so the Prophet sala lahu alihi wa sallam asked him what did he pray so he replied he prayed the 2 rakat of sunnah of fajr that he could not pray before the fardh so the Prophet stayed silent n did not forbid him from doing so, So if a person misses his sunnah of fajr he can make them up right after fajr , even though its makrroh time.
Same with sunnah of dhuhr , as it was proved from the Prophet sala lahu alihi wa sallam that He once entered the house of one of his wives after ASR n prayed 2 rakats so she inquired why had he prayed at the makrooh time n He sala lahi alihi wa sallam replied that he had missed the sunnah after dhuhr salah as such and such person from a certain tribe came to him n he got busy with him n could not pray of forgot to pray, so he made them up after asr even though it is makrooh time.
It is really sad to see brothers , specially pakistani n indain brothers in fajr salah when they get to the masjid n imam is leading fajr prayer they start praying the sunnah at the back of the masjid n they pray it quickly so they can get to the rakat , It is forbidden n not accepted as there are many hadiths where the prophet has declared that when the Fardh salah is beng performed then there is no other salah , but May Allah guide them they do not know this and when told do not want to listen coz they have gotten so stubborn , n they fall into something the messenger sala lahu alihi wa sallam has forbidden.They could pray it afyer wards or even after shurooq when time for dhuha comes in but they dont n pray it whil ethe imam is leading.
And most importantly one can pray at makrooh times the FARDH prayer if one has missed from the same day , as it was proved from the prophet sala lahu alihi wa sallam that whoever sleeps or forgets tro pray should pray when he wakes up or remmbers so even if its makrooh time one has to pray.
These were some of the exceptions , i am not sure if the suunah that the prophet used to pray before n atfter going on a safar/travelling , he used to pray 2 rakats n when comming back used to pray 2 rakats , im not sure if these can be prayed at makrroh time or not, it is a sunnah proved from the prophet sala lahu alihi wa sallam, i will ask about it InshahAllah.
But other voluntairy nawafil cannot be prayed its forbidden