Hello Woojung,
I'm happy to know your plans for your vacation. I hope that you will enjoy your trip together with your family. please take some pictures with you. ^_^
Anyway thank you for submitting your homework and please take note of my corrections. ^_^
Plans for winter vacation: -Correct
1. Go to ride a ski
Correct: 1.Go skiing
** try to make your sentence simple.
** don't use some accessory words to avoid some grammar error.
2. Go to ride sled
Correct: 2. Go ride a sled
** like the first sentence the word "to" is unnecessary for this sentence.
** The article 'a' is used when the following word is a singular noun
3. Go to Christmas vacation to England
Correct: 3. Go to Christmas vacation in England.
** Instead of using the word "to" replace it with the preposition "in".
4. Play with my friends -Correct
This is all what I am thinking plans for winter vacation.
Correct: This is all what I can think for my plans for winter vacation .
** Be careful with your sentence construction.