On those short winter days over the Christmas and new year holiday, much people enjoying resting at home and eat traditionally foods; turkeys and all trimmings, the fruit cakes, the plum pudding, and minced meat pies. To sit by the fire is also a benefit as the weathers usually cold than but some people are liking participating in winter sport.
1. Determiner error:
As we are in winter right now, the short days are close at hand, so use "these" instead of "those." Some people may not have taken this paragraph to be about this winter in particular. In that case, "those" may be correct.
New Year is a proper noun, so it needs capital letters.
3. Quantifier error:
"Much" is used with uncountable nouns. Since "people" can be counted, use "many."
4. Verb form:
For typical or repeated activity, use the simple present tense. People "enjoy" things. And since they enjoy things, you need a noun as the object. In this case, we need the gerund: enjoy "resting" and "eating"
5. Word form error:
Before a noun use an adjective not an adverb. Change “traditionally” to “traditional.”
Since "traditional foods" is followed by a list of examples, you should use a colon to introduce them. a dash would also be appropriate here.
7. Plural or singular:
Most people need only one turkey and one fruit cake, so keep these nouns singular.
8. Article use:
"All the trimmings" is an idiom that takes the definite article ("the"). "Fruit cakes" and "plum puddings" may also use the definite article (to indicate that these are familiar kinds of foods), but the result is a little stiff.
9. Word form:
This is tricky. The correct word is 'mincemeat.' It sounds the same as 'minced meat,' but is quite different. Mincemeat is a mixture of fruit in a sweet sauce.
10. Gerund or infinitive:
"To sit" is grammatically correct, but it is more usual to say "sitting" in this context.
11. Noun or adjective:
"A benefit" is correct, but the more usual usage here would be the adjective "beneficial."
12. Word form:
"Weathers" is not a plural; here the meaning is "weather is" which can be contracted to "weather’s."
13. Word confusion:
When you are referring to a time, use “then.” “Than” is a word used in comparisons.
14. Verb tense:
This is similar to (4) above. When something is generally true use the simple present tense and not the present progressive, change "are liking" to "like."
“But” introduces an independent clause, so use a comma before it.
On these short winter days over the Christmas and New Year holiday, many people enjoy resting at home and eating traditional foods: turkey and all the trimmings, fruit cake, plum pudding, and mincemeat pies. Sitting by the fire is also beneficial as the weather’s usually cold then, but some people like participating in winter sport.