If you already have an existing business relationship with your supplier, you can of course hand over your Purchase Order to your supplier at the Trade Fair. It is a convenient way to do it and you could even discuss certain details from your P/O with the supplier in case they don’t understand something.
In general, I strongly advise against placing your orders with new suppliers during Trade Fairs. It is much too risky, especially since you have not received any proper samples yet. Orders should only be placed with new suppliers after you have received their samples and checked for compliance to your company’s specifications. Also, only after passing quality control tests by your QC department or an appointed laboratory.