Is it true that if believers enter Hellfire on the Day of Resurrection, it will become cool and peaceful for them, just as it was for our master Ibrahim (peace be upon him), and that this Hadith is found in Musnad Imam Ahmad ibn Hanbal?

The Hadith you mentioned about entering the Fire was narrated by Imam Ahmad, and its wording states that entering means going in. No righteous or wicked person will remain but will enter it. It will then be coolness and peace for the believer. Then Allah will save those who feared Him. Scholars have differed in their judgment of its authenticity, some deeming it weak and others good. This Hadith, if authentic, does not contradict the texts indicating that some disobedient believers will enter the Fire to be punished therein and then emerge from it, because the Hadith specifically refers to those whom Allah does not intend to punish with the Fire.