I've replaced my previous stem with a Thomson Elite X4, which exposes the steerer tube (image from the www, for illustrative purpose).

Should I care or are steerer tubes usually factory protected against corrosion. If a surface coating should be applied, what would do best?

The steerer is generally anodized which should offer sufficient protection.

If it's a steel steerer you might want to paint it (not grease) to protect against rust. If it's an aluminum steerer, corrosion shouldn't be a problem and you might paint it only for appearance. If it's a carbon steerer (the picture is obviously not) corrosion isn't a problem and the color will automatically match.

That is interesting-- my guess is that the stem was designed with the idea of carbon steerer tubes in mind. I'd be tempted to paint it black. Alloy handlebars and seat posts are not a problem so being exposed doesn't seem like a big issue.

What material is your steerer? It looks like aluminum. Corrosion shouldn't be a problem as long as you keep salt away. If you sweat a lot, keep an eye on it, perhaps taking the stem off periodically and looking for white powder build-up in one place - a sign that galvanic corrosion is taking place. If you see it, take it seriously.

If it is steel, the corrosion is much more obvious. Rust. Not nearly so incidious.

Ben

If it visually, really bothers you (obsessive) paint the metal.

Corrosion will probably be less in the exposed area than in clamped area, or under those spacer rings where any moisture would become trapped.