No. Anything you provide of value, whether in cash or not, to your employees as compensation for their services, is considered taxable wages and must be included on their W-2. The only exceptions are certain fringe benefits provided under the regulations found in publication 15-b.
15-b includes certain situations in which you can provide meals for your employees and deduct the entire expense as a business expense to you, while not including the value in their taxable wages. A cash bonus at Christmas time does not fit any of these situations.
https://www.irs.gov/publications/p15b#en_US_2020_publink1000193706
Therefore, what you should have done was to include the Christmas gift in their box W-2 box 1 wages, where it would be subject to withholding for federal, state, Social Security, and Medicare taxes. Then, since the entire payment is treated as a wage bonus, the entire amount is a deductible business expense to the business.
You should probably consult a professional tax advisor, but I suspect that you need to issue corrected W-2s to all your employees who received these bonuses, and you will also need to send the IRS corrected form 941s for your company, As well as filing an amended business tax return. Your employees will all have to file amended tax returns to report the additional wages.
