He presumably (but not incontrovertibly - Wikia as usual is wrong and has non-referenced information presented as "fact") was the head of house because when heads of houses met during Snape's flight, Slughorn was there.
“Minerva!” said a squeaky voice, and looking behind him, still
shielding Luna from flying spells, Harry saw Professor Flitwick and
Sprout sprinting up the corridor toward them in the nightclothes,
with the enormous Professor Slughorn panting along at the rear. (DH, Ch 30 - this is even BEFORE Snape escapes and stops being Headmaster, while he's fighting McGonagall)
... and, later on, Minerva seems to act towards Slughorn as a head of house as well:
“I shall expect you and the Slytherins in the Great hall in twenty
minutes, also,” said Professor McGonagall. “If you wish to leave
with your students, we shall not stop you. But if any of you attempt
to sabotage our resistance or take up arms against us within this
castle, then, Horace, we duel to kill.”
“Minerva!” he said, aghast.
“The time has come for Slytherin House to decide upon its
loyalties,” interrupted Professor McGonagall. “Go and wake your
Later he returns back after escorting his students out and duels Voldemort (with McGonagall and Kingsley).
In addition, earlier, after Dumbledore is killed at the end of HBP, he's called to represent his house with other heads of houses by Acting Headmistress McGonagall:
'Thank you, Hagrid,' said Professor McGonagall, standing up at once and turning to look at the group around Bill's bed. 'I shall have to see the Ministry when they get here. Hagrid, please tell the Heads of Houses – Slughorn can represent Slytherin – that I want to see them in my office forthwith. I would like you to join us too.' (Half-Blood Prince, Chapter 29 "The Phoenix Lament")
All in all, while it's never explicitly stated, we see him act and be put into positions as if he is the head of house.
Since the question wasn't clear, I covered Year 7 (Deathly Hallows).
However, in Year 6 (HBP) Snape is unquestionedly the head of Slytherin house:
"I am his Head of House, and I shall decide how hard, or otherwise, to be," said Snape curtly. "Follow me, Draco." (Half-Blood Prince, Chapter 15: The Unbreakable Vow)