There's an everstone you get at the beginning of the game. Give it to your eevee and level it up. The more you level it up the more likely you are to get a glaceon.
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You cannot evolve an eevee in to a glaceon. You have to trade one from Pearl, Diamond, or Platinum.
eevee
In Pokémon HeartGold, you can only evolve Eevee 5 ways which would be: Using a Fire Stone on an Eevee into to evolve it into a Flareon, use a Thunderstone on Eevee in order to evolve it into a Jolteon, use a Water Stone on Eevee in order to evolve it into a Vaporeon, evolve it into Umbreon via level-up at night (which is between 8PM and 4AM) when it's happy enough and evolve it into Espeon via level-up during the day time. You can also evolve Eevee into Glaceon and Leafeon however evolving Eevee into Glaceon or Leafeon is not possible in "HeartGold" or "SoulSilver," Eevee can only evolve into Glaceon via level-up when it's near the Ice Rock which can only be found in the Sinnoh region near Snowpoint City and Eevee can only evolve into Leafeon when it's near the Moss Rock which can only be found in the Sinnoh region which is in the Eterna Forest.
Go to the ice rock by snowpoint city and in the grass around it level up your evee by 1 level, it doesnt matter what time or happiness just level it up by 1 and it will evolve (MUST BE NEAR IT)
You will get an eevee egg. That you can evolve into an eevee or the other eevee evolutions.