Who says he couldn't?
Consider the facts:
In Order of the Phoenix Dumbledore made a portkey from Hogwarts to Grimmauld Place and a portkey from the Ministry to Hogwarts, and there is no mention that he had to first remove any preventative enchantments in order for the portkeys to work.
In Goblet of Fire Barty Crouch Jr. created a portkey that took Harry out of the school grounds and later returned him to the school grounds. If there was some protective enchantment that prevented portkey travel to and from Hogwarts, it would seem to be unlikely that Crouch Jr. would have the ability to remove it.
When discussing how the other schools would arrive in Chapter Fifteen of Goblet of Fire Ron suggested portkeys and Apparition:
"A Portkey?" Ron suggested. "Or they could Apparate – maybe you're allowed to do it under seventeen wherever they come from?"
Hermione only objected to the Apparition suggestion, implying that it is possible to portkey into Hogwarts:
"You can't Apparate inside the Hogwarts grounds, how often do I have to tell you?" said Hermione impatiently.
If we look carefully at what Hermione tells Harry when he thought Voldemort had transported him to London, we see that she says nothing to imply that Voldemort couldn't get into Hogwarts with a portkey:
“One day,” said Hermione, sounding thoroughly
exasperated, “you’ll read Hogwarts, A History, and
perhaps that will remind you that you can’t Apparate
or Disapparate inside Hogwarts. Even Voldemort
couldn’t just make you fly out of your dormitory,
All she says is that Apparition is prevented and that Voldemort couldn't make Harry fly out of his dormitory.
Based on all the above, it would seem that Voldemort could have used a portkey to enter Hogwarts. However, in Chapter Twenty-Seven of Half-Blood Prince, Dumbledore seems to think that Hogwarts is impregnable:
"But you were saying... yes, you have managed to introduce Death Eaters into my school, which, I admit, I thought impossible.... How did you do it?"
Given that it is unlikely that Dumbledore simply overlooked portkeys, this might seem at face value to indicate that Voldemort would not have been able to enter Hogwarts via portkey. However, we can perhaps resolve this potential contradiction by suggesting that Dumbledore didn't mean that no form of entry into Hogwarts was possible; rather, he meant that he thought it impossible for Malfoy to bring Death Eaters in, which would at most tell us that he didn't think Malfoy capable of creating a portkey into Hogwarts.
So why didn't he?
If it is true that Voldemort could have entered Hogwarts via portkey we now have to explain why he didn't. The answer to this may be that he didn't need/want to:
- Philosopher's Stone – he was already in Hogwarts on the back of Quirrel's head.
- Chamber of Secrets – He was powerless and had no reason to enter Hogwarts.
- Prisoner of Azkaban – He was powerless and had no reason to enter Hogwarts.
Goblet of Fire – The only reason for him to enter Hogwarts would be to kidnap Harry, and in Chapter Thirty-Three he says why he didn't do this:
And then, the boy would return to Hogwarts, where he is under the crooked nose of that Muggle-loving fool from morning until night. So how could I take him?
He did not say that he could not gain entry to Hogwarts; he merely said that Dumbledore would be watching Harry too closely for Voldemort to kidnap him.
Order of the Phoenix – As explained in Chapter Five, Voldemort was trying to keep his return a secret:
“Because he doesn’t want to draw attention to himself
at the moment,” said Sirius. “It would be dangerous
for him. His comeback didn’t come off quite the way
he wanted it to, you see. He messed it up.”
“Or rather, you messed it up for him,” said Lupin with
a satisfied smile.
“How?” Harry asked perplexedly.
“You weren’t supposed to survive!” said Sirius.
“Nobody apart from his Death Eaters was supposed to
know he’d come back. But you survived to bear
The idea that Voldemort wouldn't venture into public, guarded places is reiterated in Chapter Thirty-Five:
“Get it himself?” shrieked Bellatrix on a cackle of mad
laughter. “The Dark Lord, walk into the Ministry of
Magic, when they are so sweetly ignoring his return?
The Dark Lord, reveal himself to the Aurors, when at
the moment they are wasting their time on my dear
Additionally, at this point Voldemort wasn't really ready to confront Harry yet, as he still needed to hear the prophecy.
Half-Blood Prince – Voldemort had no particular need to enter Hogwarts. He had Malfoy assigned to kill Dumbledore, with Snape as a back-up. He could be pretty confident that Dumbledore would be dead soon, without him having to do anything. Venturing into Hogwarts would only have been an opportunity to get caught.
Additionally, Voldemort was always supposedly afraid of Dumbledore, which would add to his reluctance to enter Hogwarts. For instance, as Harry tells Slughorn in Chapter Four of Half-Blood Prince:
"I reckon the staff are safer than most people while Dumbledore's headmaster; he's supposed to be the only one Voldemort ever feared, isn't he?" Harry went on.
And Slughorn more or less agreed:
Yes, it is true that He-Who-Must-Not-Be-Named has never sought a fight with Dumbledore," he muttered grudgingly.
Or as Ron said in Chapter Eleven of Half-Blood Prince:
"But Hogwarts is safer than their homes, bound to be! We've got Aurors, and all those extra protective spells, and we've got Dumbledore!"
Or has Hagrid said in Chapter Four of Philosopher's Stone:
One o' the only safe places left was Hogwarts. Reckon Dumbledore's the only one You-Know-Who was afraid of. Didn't dare try takin' the school, not jus' then, anyway.
So in conclusion we could say that Voldemort perhaps could have entered Hogwarts via portkey if he really wanted to, but he simply didn't consider it a purposeful endeavor.