Since I installed Dawnguard there are random freezes of the game. The whole screen freezes and I have to quit the game with the Task manager.
Is there any solution for this problem?

you are not alone.

Same here its quite annoying to have a high end system freeze on you like this.

If you are on a PC, then check your mods.
I had a problem with my Saves made on this PC with SOS Civilization when the Saves were transferred to my Gaming Laptop. The Save was Bloating and using all of the available Ram every few seconds.
I also enabled Script Logging and had that cause periodic Lags/freezing in game.

Having the same problems. Seems to occur mostly when entering/exiting buildings and dungeons etc., but have had it happen randomly out in the wild as well. Occurs with no mods / vanilla Skyrim.

Edit: My save file sizes seem fine, 8-9 megs

@ bradleyh

But the problem is since Dawnguard. Why should my other mods suddenly create a complete freeze (not a CtD) of the game?

The content and scripts added by Dawngaurd can conflict and cause errors, there has also been an issue with the Sound settings.
I have issues with scripts in my Gaming PC because I forgot to remove some mods, but I have had a locked Loading Screen Once (After I had a very bad stuttering problem caused by exixsting Scripts in a Saved Game). The PC I am using now only has @ 2Gb of RAM for games, everything else is being used by background applications. When I play with this PC, I have locked Loading Screens every hour. My Gaming PC has enough RAM to reduce this time to six or eight hours.
The Game does use alot of Memory during a cell transition, if our computers can not eliminate the old Data, and Load the New Data, We get a locked Loading Screen.
I blame some of this on Bethesda, but poorly written or outdated Mods make the Bethesda mistakes worse.