Most bodhráns are made with a goat skin. Goat skin is particularly sensitive to humidity and temperature. If the weather is hot/dry, then the skin shrinks and tightens. This gives a pingy, high note. If the weather is humid, then the skin sags and the note gets low and boomy. Usually, we need something in between, so adjustments to the skin are required. The classical way to soften a dry drum is to apply moisture - usually water. This loosens the skin and we get the deeper note. Alternatively, when the weather is damp, we need to heat/dry the skin in some way e.g. place it near a heater or use a hair dryer.
The more modern way is to buy an adjustable drum, which lets us tighten or loosen the skin by turning screws or levers, or pushing cams. The adjustable drum removes the need for water or hot air. In extreme conditions, the drum will not adjust sufficiently, and then we're left with the water or the air....
Repeated applications of water or hot air will generally deplete the natural oils in the skin. This will result in a dry, brittle, hard skin. So we have to find some way of adding some moisturising/conditioning to the skin which will not be damaging in the long term.
Different recomendations are made, here. The general opinion is to use lanolin in some form. Lanolin is an oil that exists naturally in goat hair/skin, so it seems a good place to start. Various forms are available, in the US you can buy Aqueous Lanolin in pharmacies.
Another favourite is Dubbin. Dubbin is used to waterproof shoes and boots, and can usually be found in sports equipment shops.
My main experience, here, is in the use of dubbin, which I have used to soften new, hard skins, and to 'top-up' naturally drying skins. I generally apply the dubbin to the inner skin.
I have encountered bodhráns that were treated with linseed oil. I would avoid this at all costs. The oil builds up into a sticky gum that holds the inner hand to the drum. Not a pleasant or fruitful result.
In terms of storage, make sure that the drum is left in a looser state, if tunable. The reason is quite simple. If it is tight and the weather dries, then the skin/tacks/glue may rip.