Planting Trays as Mini Greenhouses

I have no greenhouse, and limited indoor window space with poor lighting. So I am thinking about wrapping clear plastic around the planting trays as a kind of mini-greenhouse, bringing the trays inside overnights. Would this idea work okay?

Yes, this idea can work well. The key is to make sure that the plants do not freeze, dry out, or overheat while outdoors during the day. You need to watch the ventilation: too little ventilation means a buildup of condensation and a risk of contracting fungal diseases. Harmful temperature fluctuations can also be a problem: a small volume of air in the "greenhouse" can heat up very quickly.
In our zone (zone 5), a mini-greenhouse works well in April and May the month or two before the last frost date in our area.