While it might seem tempting, keep the pink yarn for practice or for your in-barn fun Valentine's Day show. Hunters should be turned out conservatively, and bright, colourful yarn will detract from your performance. Some riders like to have a "lucky braid", one braid that is done in a different colour, usually at a specific location on the neck. If done tastefully, this is acceptable in the show ring.
The ideal colour will be about the same as your horse's mane. If your horse's mane is a blend of colours, or if the ideal colour isn't available, a darker yarn will usually look better than a lighter one. If you will be braiding a pinto with white in its mane, have two colours of yarn handy so that you can use the one most appropriate for each section of hair.
If you will only be braiding one horse, you can choose the colour that is best for that particular mane. If you braid many horses or don't know the horses that you will be braiding, it can be easier just to keep a stock of limited, multi-purpose colours. Most manes can be done in black, off-white or a medium/dark brown. Off-white is usually a better choice than bright white because even when clean, most light-coloured horses are not truly white and can be made to look yellow by a too-white yarn.
The table below shows the most common horse colours along with the colour of yarn that I would choose for each one. All of the yarns shown are from my favourite brand, Bernat Satin. The middle column shows the best-matched colour from that collection while the column on the right shows only black, off-white and medium/dark brown. I like the strength and amount of stretch of the Bernat Satin, but you should try a few different brands to get a feel of what works best for you.
Some braiders will use a very dark navy in black manes to make it easier to distinguish between the mane and the yarn when removing braids. If it doesn't stand out, this is acceptable.