Of course you can cover them, although I think they'll be fine. The rain certainly won't hurt them. And if they are very small the 29 degrees may be OK too as they are near the earth which should be a bit above freezing if it has been sunny in the daytime. On the other hand what have you got to lose by throwing an old sheet or some newspapers over them?

Thanks! I thought the moisture would make the freezing temps that much worse? In any case I was almost sure 29 degrees would do them in. I guess there's more hope than I thought.

Unfortunately it hasn't been sunny here for a few days. Quite a change from the warm sunny days of the last few weeks.

Nasturtiums are frost hardy and will withstand a few degrees of frost. If it's raining it won't freeze close to the ground. Covering them with something that can be beaten down to the ground will crush the plants with the weight of the water. A trick experienced gardeners use when an unexpected frost hits is to water the plants early in the morning before the sun hits it. This washes the frost off and prevents frost damage. It has saved many a tender plant for me. Frost alone does not kill plants. Frozen plants die when the sun hits them. It bursts the frozen cell walls. Watering the plants thaws the frozen cells and brings the plant to just above freezing. Have you ever seen pictures or orchards when the weather is frosty. They turn on their sprinklers for the same reason

Sometimes I have lined the inside of some planting pots or containers with newspaper (basically lay the newspaper in the pot and make it loosely conform to the pot's inside shape), then I turn them upside down on the plant or seedling to protect it. If winds are strong, I also put something heavy on top of the pot. This gives it some kind of newspaper insulation but not let the newspaper crumple down on the plant.

This may or may not allow the plant to breathe properly, depending on the pot's contact with the soil, so this is only intended for short duration protections, such as overnight. In theory, the pot's contact with ground is not air-tight and there are drain holes in the pot that, but to be safe, just use it for short durations.