The first pic is a little unfair. If you look at the sidewalk, it appears to have been raining. Barack is trying to keep Michelle and himself covered, as opposed to ducking the umbrella through the gate and getting sprinkled. It doesn't appear to be a torrential downpour, so a little sprinkling wouldn't hurt, but I understand the impulse.
Michelle's a big girl and could probably survive a few raindrops. From the look in her eyes, though, that might not have seemed a prudent course of action for Barack at the time.
If it had been Hillary, of course, there would be the risk of melting, so it would be an entirely different calculation.