Is it possable to trade Pokemon to Pokemon white from Pokemon hart gold.?

You can't trade Pokemon from any of the other games to Pokemon Black and White. Instead you have to wait until you've beaten the game and unlocked the PokeTransfer. To do this after beating the game head to Route 15, there should be an odd building. Go inside it and a scientist will talk to you. He'll explain about the PokeTransfer and how it works. You'll need two DS to Transfer your Pokemon over. One with Black/White game and one with your Heart Gold or other Pokemon DS game. When you connect you Pokemon Black or White game it will send out a DS download play which will let you send over the Pokemon you want from your Pokemon Soul Silver to your Pokemon Black game. After you've done that you can play a mini game to catch the Pokemon. If you send the three event Dogs or Celebi over this way their events will not trigger. You'll have to send them over by using the Relocator. To Unlock the Relocator you need to go to Castelia City and find the guy who asks for a phrase, he'll be in the building that has a Hiker and a Pikachu on the first floor. Tell him "Everyone Happy" Simple Connection." This will unlock a feature on the game menu that lets you use the Relocator, which again you need two DS game systems to use. Again a download play will be sent out by your Pokemon Black or White game. You pick up the Download play on the DS's menu that holds Your Pokemon Soul Silver, Heart Gold, Diamond, Pearl, or Platinum game. This will send over the three shiny Dogs and Celebi as long as their in your PC.

No but you can transfer Pokemon from heartgold to Pokemon white after you beat the elite four

It is, but you must defeat the Elite Four and N. Then go to the route west on White Forest/Black City and find the laboratory. (You need two DS.) When the Black/White game is ready, go on the other DS to download play, and select the Pokemon to be traded.