I haven't tried freezing it but I'm 99.9% sure it will be fine. Hope you enjoy it!

I've never actually eaten an orange cauliflower so I'm not sure how much the flavor differs. I doubt if it's much different. All it will really affect is the color of the soup. I don't see why it wouldn't work. As far as the horseradish goes, you can add as much or as little as you like, tasting as you go to get th ebalance just right for you.

Why would I publish a non-vegan recipe on a vegan website? I am vegan and would never promote the use of animal products in my recipes and giving the recipe only 2 stars when you haven't even made it isn't a very fair thing to do at all. The horseradish sauce I link to is vegan. It is called Atomic Horseradish and I have a jar in my fridge. Here is the ingredient list: distilled vinegar, water, parsnips, horseradish, salt, sugar. As for the vegetable broth which is Pacific brand, the ingredients in that are water, carrots, tomato, celery, onions, garlic, leeks, sea salt, bay leaves, parsley and thyme. No beef. Bear in mind that I use Amazon.com for my links because the majority of my readers are in the U.S. If you are outside of the U.S then when you click on the links Amazon takes you to a general page with multiple items that IT thinks may be relevant. Common sense should tell you that I wouldn't be linking to animal based products.
When making a recipe you do not have to use the products I link to anyway. You can buy whatever horseradish sauce or broth that you like. I provide the links to be helpful so that people can see what I use when I make the recipes and so that they don't have to contact me to ask every-time.