during january 1-3

[billmcd]

And what about:
Will it be incorrect to use 'on' before this period?

Use of "on" would be a reference to one specific date.

[kvvic]

So the use of 'on' in the above sentence is incorrect. Actually I also know that 'on' refers to one date but I saw many examples where 'on' was used as follows:

...prizes, cameras and toys await the winners of the Boots Northern Ireland Children of the Year competition to be held on the 7-11th of September.

Don't forget to visit the Yarn Fair for London, the South and South East at the Old Loom Mill, to be held on 17–20 September.

On Jan. 25 a debate in the Assembly of Bosnia-Hercegovina ... endorsed a referendum on the republic's sovereignty to be held on Feb. 29-March 1.

These sentences are from the British National Corpus (some newspapers), which means they are supposed to be correct.
Is 'on' here also used incorrectly? Or is there some difference between the way 'on' is used in these sentences and in mine?

[5jj]

These sentences are from the British National Corpus (some newspapers), which means they are supposed to be correct.

No it doesn't. It simply means they have been used. I don't usually go to newspapers for examples of good writing.

'On' is undoubtedly used in the way that you note. Most of us do not consider that to be correct. As you wrote in your first post, "My feeling is that although the meaning is probably clear, it's not the right word to use here."

[kvvic]

Could you please correct one of the above sentences to give me an example of how you would express the same idea?

[5jj]

susiedq and billmcd have already made suggestions, above, for this type of situation.

[kvvic]

As far as I understand, the correct ways would be:
1. Don't forget to visit the Yarn Fair for London, the South and South East at the Old Loom Mill, to be held 17–20 September.
As per susiedq's suggestion.
2. Don't forget to visit the Yarn Fair for London, the South and South East at the Old Loom Mill, to be held during the period 17 to 20 September.
As per billmcd's suggestion.
3. Don't forget to visit the Yarn Fair for London, the South and South East at the Old Loom Mill, to be held from 17 to 20 September.
My option.
Are all these sentences correct? Is No.1 not too informal?