In a small, heavy-based frying pan, dry-fry the coriander seeds, cinnamon stick and mustard seeds until fragrant, stirring often to prevent burning. Set aside the dry-fried spices. Once cooled crush roughly in a pestle and mortar.
Put the apples, onions and garlic in a food processor. Process to about 1/4in chunks. Transfer the apple mixture to a large non-reactive saucepan.
Place the horseradish in the food processor. Process to a fine paste. Add the horseradish to the apple mixture in the saucepan.
Add the crushed spices, the sweet and hot smoked paprika, sugar and red wine vinegar and salt.
Bring everything up to simmering point, stirring all the time. Once the mixture is simmering, reduce the heat and let it cook uncovered very gently for three and a half hours, until the mixture has thickened and all the liquid has evaporated
Use a wooden spoon to make a trail across the top of the chutney. If the trail fills with juice then the chutney is not ready and needs simmering further. If the trail does not fill with juice then the chutney is ready.
Spoon the hot chutney into four hot, clean jars. Cover the jars with waxed discs and set aside to cool, then cover and seal. Label and store in a cool dry place for up to six months.