Combine cucumber, carrot, celery, onions, sweet red pepper, and cauliflower in a large glass, ceramic, or stainless steel container. Dissolve salt in water; pour over vegetable mixture. Cover and let stand in a cool place 12 hours. Rinse and drain 3 times.
Combine vinegar, sugar, hot red pepper, and mustard and celery seeds in a stainless steel stockpot. Bring to a boil; boil 3 minutes, stirring until sugar dissolves. Add vegetables. Reduce heat; simmer, stirring gently several times, until thoroughly heated.
Pack vegetables into hot sterilized jars; cover with syrup, leaving 1/2-inch head space. Remove air bubbles. Cover with metal lids, and screw bands tight. Process in boiling-water bath 15 minutes.
Note: The spices may be tied in a cheesecloth bag and discarded before packing into jars.