Here is what you should do:
1. Sand them down and fill any cracks or splits or depressions in the wood with an ACRYLIC caulk. You want to fill in any depressions so that any water runs off the sill instead of puddles on it. And, acrylics have the ability to allow water molecules to pass through them, but not liquid water. That means that any moisture that does get into the wood can evaporate through the acrylic caulk, but any rain water or snow melt that comes in contact with the acrylic caulk won't get into the wood. Thus, acrylic caulk acts as a check valve to allow moisture out, but not allow water in, thereby keeping the wood as dry as possible.
2. Treat the wood
And you do this in two ways:
A) Drill a hole into the sill near each bottom corner and install a borate rod. Plug the hole after inserting the rod. Use Permagum (which you can get at any appliance repair shop for caulking the joints where wiring or tubing goes into or out of a freezer compartment, or just use a wood or rubber plug (or even some acrylic caulk, maybe). The hole should be drilled and the rod inserted to ensure maximum exposure to the end grain of the wood. That's because wood absorbs liquids 15 times faster through it's end grain than across it's grain.
Borate based wood preservatives are popular amongst people who have log homes here in North America because borates have the ability to penetrate through the wood (including the heartwood) to make the entire cross section of the wood resistant to rot. What happens is that when the wood gets wet, then the borate rod dissolves, releasing borates into the wood which are poisonous to most fungi, including the wood rot fungus, Serpula Lacrymans. You can order borate based wood preservatives if you use Google to find "Boracol" liquid borate based wood preservatives or "Impel" solid borate rods. Unfortunately, borates are soluble in water, so once the borates permeate through the wood and get to it's surface, they will then be washed off by rain water IF you don't maintain a coat of paint on the window sill to prevent that (or put a metal cladding down over the wood to prevent the borates from being washed away).
B) Paint the surface of the window sill with an end cut preservative like zinc or copper napthalate. This will prevent wood rot on the surface of the wood with a wood preservative that won't be washed away.
3. Now paint the wood.
Since you already have an oil based product (zinc or copper napthalene) on the surface of the wood from the end cut preservative you applied, a latex primer won't stick, so use an EXTERIOR alkyd primer to prime the wood. Exterior alkyd primers will dry porous so that moisture in the wood can evaporate through them.
Then, top coat over that with a flat water based paint. Flat paints allow moisture to pass through them more readily, allowing any moisture in the wood to dry out faster.
By doing the above, what you have is a wood window sill that is protected from rot on it's exterior by copper or zinc napthalene which will not be washed away by rain or melt water from snow. Also, if any water does get into the wood, it will cause the borate based Impel rods to dissolve, releasing borate based preservatives into the wood. These borates will permeate the wood very quickly if it's wet, up to a centimeter per day. None of those borates will be washed away until they penetrate through to the top surface of the sill, and then only if they come into contact with water. You can prevent that by maintaining a coat of paint on top of the wood to prevent the borates from coming into contact with the water. (Besides, you'll only START to lose borate once everything under the surface is saturated with borate and fully protected from wood rot.) And, the coatings over the wood all allow moisture to escape from the wood without allowing liquid water to enter the wood, thereby keeping the wood as dry as possible.
And, if you want to go one step further, screw metal cladding onto the sill to prevent any rain or snow melt or UV light from the Sun from deteriorating the paint. Normally I don't like metal cladding because it can trap moisture IN thereby promoting wood rot. However, if you're using Impel rods that will dissolve in any moisture that gets into the wood, then that moisture won't do any harm because any water under that metal cladding will be poisonous to fungii, including the wood rot fungi. So, the wood can last for hundreds of years underwater, just as some ancient shipwrecks do.
Or, at least, that's what I'd do.
Post again if you want me to explain my reasoning in any of these steps.
