You can certainly experiment with essential oils in your winemaking if you remember the old adage that “oil and water don’t mix.” Essential oils are the natural distilled volatile aroma compounds from fruit, leaves, and flowers, and are used in the perfume and cosmetics industries, among others. Essential oils are easy to find online or in health food stores and are relatively inexpensive, costing between $10-$15 for a small 1 oz. (30 mL) bottle. The most common essential oils include lavender, peppermint, and rosemary, but a huge host of oils is available online.
Why would anyone want to use essential oils in winemaking? As you suggest, it might be interesting to add some additional flavor and aroma highlights to your wines. However, be advised that since the molecular weight of most essential oils are so low, what’ll happen is the oils will actually “sit on top” of your wines, and not truly absorb or mix into solution. It’ll be as though you’ll have an actual oil slick on top of your carboy or wine bottle. Open a bottle of wine with essential oils on top and you’ll likely pour most of the oil off into the first glass, making that first whiff a doozy for whoever sticks their nose in.
Essential oils also evaporate quickly, meaning that if you put some oils into a barrel with your wine in it, much of the oil’s potency will be lost by a) absorbing into the wood and b) volatilizing (evaporating) into the air. Not very effective. So do oil and wine mix? Not so much. I’d leave the essential oils to perfumers and aromatherapists or when dealing with high-alcohol solution for making herbaceous apertifs. I suggest mixing some lavender essential oil with some unscented almond or olive oil and make a massage rub for yourself. After all, oil and oil do mix.