Transportation to Harbin festivals during Chinese New Year

About this festival, the best collections of ice artworks are mainly exhibited in the following five places: Ice and Snow World, Ice Lantern Garden Party, Sun Island Scenic Area, Yabuli International Ski Resort and Zhaolin Park.
And yes, you are right. There will have crowded local people and tourists during that time. But the transportation won't become much difficult than normal time. You are suggested to start off to the scenic areas early. And the prices won't be much higher. Most people can acceptable that. Don't worry.
In addition, about the entrance tickets:
1. To Ice and Snow World:CNY330 for adult during New Year’s Day and Spring Festival
2. To Ice Lantern Garden Party: CNY 60 per adult
3. To Sun Island Scenic Area: CNY 240 per adults
4. To Yabuli International Ski Resort: About CNY 150 to 300 for two hours
5. To Zhaolin Park: CNY60 per adult

Thank you. Any suggestions about getting tickets for the ice slides and also the price for the horse drawn sleigh ride? Your service is most appreciated.

The service fee varies from one spot to another. Generally, it is CNY 80-100 per person for the horse drawn sleigh ride. For ice slides, there are many free ice rinks, one of the most popular is at Songhuajing River. You can go and try. But you may need to rent some entertainment facilities; that will need some money but sorry I'm not very clear about the rate.