Well, you could hardly have made the letter more formal.
However, maybe I can make a few suggestions that will be helpful.

Originally Posted by
hookeba
First, we would like to give our warm welcome and wishes of good health and prosperity to your esteemed company
Try:
We would like to extend our warm welcome and wishes of good health and prosperity to everyone at (name of company).

Originally Posted by
hookeba
In business, small and elegant gifts for customers or business associates work as a catalyst for tightening business relationships. Likewise, presents for employees at holidays shows their bosses' appreciation for the staff's contribution to the company
Try:
In business, small and elegant gifts for customers or business associates work as catalysts for tightening business relationships. Likewise, presents for employees at holiday time show their bosses' appreciation for the staff's contribution to the company
(presents...show)

Originally Posted by
hookeba
As a professional and seasoned wine and spirits purveyor in Indochinese market, we are pleased to introduce you a wide and diverse category of wine and spirits ranging from mainstream products to fast-drink cocktail and fizzy fruit juice, from world famous products to new and high quality ones at reasonable prices.
Try:
As a professional and seasoned wine and spirits purveyor in the Indochinese market, we are pleased to introduce you to a wide and diverse category of wine and spirits ranging from mainstream products to fast-drink cocktail and fizzy fruit juice, from products already world famous to new and appealing high quality products at reasonable prices.

Originally Posted by
hookeba
Enclosed you will find our quotation and a brochure of some products for the upcoming festival season. We always do our utmost to provide not only our excellent products but also our most thorough service to your company
We look forward to receiving your reply. If any enquiry, please contact…. We are pleased to send our representatives to assist you in person at official hours.
Best regards,
Perhaps:
Enclosed you will find our quotation and a brochure of some products for the upcoming festival season. We always do our utmost to provide not only our excellent products but also any assistance necessary.
We look forward to receiving your reply. If you have any questions, please contact…. We would be pleased to send our representatives to assist you in person.
Best regards,
What do you think?