This plant is a brassica/cabbage-mustard family[see below]. It really has nothing to do with horses.
In old English, horse meant: coarse, that is inedible, and we all may now understand why…………….when used as major [Ashkenazi minhag] during the Pesach Seder.
We will discuss here more the medical virtues of horseradish which has been used for centuries.
Let’s sum up here some uses and expand on these further in the article :
Sinusitis, Common cold, cough, Whooping cough, Asthma, Bronchitis, Allergies, Hay fever, Bacterial infections, Sore throat Cancer, Urinary tract infections, Arthritis, Rheumatoid arthritis, Gout, Digestive problems, Gallbladder problems, Circulatory problems.
Used as food in traditional amounts, horseradish is in general safe even for long-term use.

Don’t use horseradish for small children [under 4, as advised in the literature] and be careful with it if you suffer from an ulcer or chronic kidney disease.[can be irritating]
Avoid it also if pregnant or breastfeeding or use then only tiny bits.
In the 17th century, one found the following statement in a book: ……. “the root, sliced thin and mixed with vinegar is eaten as a sauce with meat, as among the Germans.”
For the various “prescriptions” [way of preparing and using it]: see below
As it contains a compound called sulforaphane, it is a highly protective food against cancer [ like other foods rich in sulforaphane
 such as sprouts, broccoli, watercress], especially when eaten together with fish or poultry or other compounds rich in selenium [ like eggs nuts, mushrooms, sunflower seeds etc]
Belonging to the brassica family, which includes cabbage and mustard, one might have thought it may suppress thyroid function, but this has not been shown to be the case.
Maybe one should not frequently use it with a real under function [hypothyroid ea] of the thyroid.
Horseradish is a very reliable remedy for sinus infections.
It promotes the removal of mucus from the upper respiratory passages. .
If you are prone to developing sinus infections, try taking horseradish the moment you feel a catching cold to prevent mucus from accumulating in the sinuses.
Horseradish is highly protective against foodborne illness [E.coli, listeria, staphylococcus aureus etc] preventing one from getting a gastrointestinal infection.
It helps digestion by increasing stomach acid.
It helps as a diuretic [stimulates urine production] in some cases of oedema and urinary tract infections, which also has an antibiotic effect.
As it is a potent diuretic, it was employed by old herbalists against stone-forming [kidneys,gallbladder]
Externally it can be used for inflamed joints and muscle pains in general and it also may help to heal infected wounds.
If you wish, you can buy the tincture [mother tincture of horseradish and dab a wound with it or make an infusion and use a piece of cloth soaked in the infusion on the wound.
Against [chronic]inflamed gums, one can chew grained horseradish. It can be mixed with carrots to modify the sharp taste.
For ingrowing toenails and inflamed skin around the nail bed [Paronychia ], locally applied horseradish be of great help. By stimulating bile production from the gallbladder, horseradish assists in digesting fatty foods, relieve
gastrointestinal problems and help in indigestion, colitis, poor appetite, and flatulence.
Horseradish also seems to stimulate circulation whether used internally or externally. Taken internally, it helps against poor circulation, which can cause cold hands and feet and improve general weakness.

Side effects: May cause vomiting, upset stomach or excessive sweating if consumed in large amounts.
Even a tiny taste of this potent food seems to “penetrate” your nose and brain……..

Now we will discuss some ways in which horseradish can be used in the above mentioned [or not mentioned ] conditions
Horseradish or “prepared horseradish” generally refers to the grated root of the horseradish root mixed with vinegar.
Grate the horseradish in a food processor or blender. (You can use a grater, but tearing eyes and stinging nose may make you bless your blender……….. Add honey or sugar and vinegar: about 2 tablespoons honey or sugar and 1 tablespoon vinegar per cup of horseradish.

Tincture: Buy in a pharmacy

Herbal Tea:[infusion] Steep 1 teaspoon fresh grated horseradish in hot water and sip for congestion. Add honey and lemon to improve the taste.
Use this tea for allergies-related respiratory problems, such as hay fever or persistent coughs.
Instead of a tea, one can also make a maceration [hashraya]: leave 20-30 grams of the fresh root in 1 litre of wine for 10-15 days and drink 2-3 small glasses per day

Horseradish syrup: grained horseradish root is mixed with 4 spoons of honey and let stand for several minutes. Strain the mixture through a gauze and express the gauze. The raw syrup is obtained. The remains from the gauze are boiled in a small quantity of water, strained and then left to cool off, after which this is mixed with the raw syrup. Take 3 spoons of the mixture a day.

Soak a cloth in horseradish tea and apply the fabric to a wound. Discontinue if the skin gets irritated.
Use: 20-30 grams of fresh root to 1 litre of water.
You can also use tea as a foot bath or hand bath to relieve chilblains

Mix 3-4 tablespoons of the freshly grated root with apple cider vinegar and honey to taste for bladder infections. Take the whole amount throughout the day.
For sinus infections: If you can tolerate it, hold 1/4 teaspoon of the freshly grated root in your mouth until all the taste is gone. One will feel immediate relief from the pressure in the sinuses, and the infection will start clearing up.
Or: Take 1/4 of a teaspoon of horseradish tincture in warm water. Repeat the dosage frequently to clear head congestion.

And for biologists: horseradish peroxidase, found in the plant, is used extensively in molecular biology for antibody detection, among other things.
A happy and healthy Pesach with at least a bit of horseradish, even for the S’faradim.