Hair dye can drip on your wood furniture, and while this stain can be difficult to remove, it may not ruin your pine wood furniture. Stains such as dye require the use of harsher chemicals that will also dissolve the polish and wax from the pine furniture. Be aware of this so that you can repolish and wax the furniture once you've removed the hair dye stain. Cleaning the stain as soon as possible might make it possible to avoid harsh cleaning chemicals and dissolving the polish and wax.
Remove as much of the hair dye as possible with a clean cloth. Dab the stain rather than wiping it to make sure you don't spread it.
Mix 1/2 gallon of hot water with 1 tbsp turpentine and 2 tbsp linseed oil. The turpentine and hot water will work to remove the dye while the linseed oil will condition the wood.
Put on rubber gloves to protect your hands from the heat of the water.
Dip a cloth into the solution and wring out as much of it as possible. Never soak wood, as this will only cause it to buckle and eventually rot.
Rub the cloth over the hair dye stain. Reapply the cleaning solution as needed until you remove the stain or as much of it as possible.
Apply paint thinner to a clean cloth if the hair dye stain is still visible.
Rub the cloth over the hair dye stain until you've removed it. This will likely remove the wax and polish layer.
Wipe the area with a water-dampened cloth and dry it completely with another cloth.