Step 1 In a large glass or stainless steel bowl, combine the cucumbers, cauliflower, green and red peppers, carrots and onions.
Step 2 In another large glass or stainless steel bowl, dissolve the pickling salt in 7 cups water. Pour it over the vegetables. Cover and let stand at room temperature for 1 hour.
Step 3Meanwhile, prepare the canner, jars and lids by washing and rinsing the jars and lids, placing a rack in the bottom of a boiling-water canner and placing the jars in the rack, adding water to fill and cover the jars. Cover the canner and bring water to a simmer (boiling the jars or pre-sterilization is unnecessary); keep the jars hot until ready to use.
Step 4In a colander placed over a sink, drain the vegetables. Rinse with cold running water and drain thoroughly. Add the hot yellow peppers and mix well.
Step 5In a large stainless steel saucepan, combine the garlic, 1 1/2 cups water, vinegar, sugar and horseradish. Bring to a boil over medium-high heat, stirring to dissolve the sugar. Reduce the heat and boil gently for 15 minutes, until the liquid is infused with garlic flavor. Discard the garlic clove.
Step 6Pack the vegetables and 1 to 3 jalapeno pepper halves into hot jars to within a generous one-half inch of the top of the jar. Ladle hot pickling liquid into the jar to cover the vegetables, leaving one-half inch of headspace. Remove air bubbles and adjust the headspace, if necessary, by adding hot pickling liquid. Wipe the rim. Center the lid on the jar. Screw the band down until resistance is met, then increase to fingertip-tight.
Step 7Place the jars in the canner, ensuring they are completely covered with water. Bring to a boil and process for 10 minutes. Remove the canner lid. Wait 5 minutes, then remove the jars, cool and store for 4 to 6 weeks before serving to allow the flavors to develop.