It depends on what you mean by stain.
Unfortunately the finishing world is full of proprietary product names, irregular use of similar/the same words, and to be plain, sometimes deliberately misleading terminology*.
Stain conventionally refers to a product that colours the wood and nothing else.
Today however many products that use the word stain in the name are coloured finishes (possibly the best known being "gel stain" which is a jellied coloured varnish).
If you're planning on using one of the latter then yes you can use it as a standalone finish. If you were planning on using the former then no, it's not advisable.
Also, the temperature that the stain/finish would be exposed to during the drying time may be around 45°F (~7°C).
This is a bit low for a lot of products used in wood finishing. Many different products quote a minimum figure of 50°F or 10°C during application and when drying, and ideally higher.
45°F is not excessively low though, so instead of preventing proper drying it could mean only that you can expect extended drying periods (e.g. 4-5 days instead of 1-2). It's important to note though that some product simply won't dry properly when applied in colder conditions.
So obviously the exact product you eventually go with will make all the difference here — check product literature for guidance and if in any doubt do a test in the finished setting on a scrap of the project wood, and be guided by the results.
*The infamous "Tung Oil Finish" is perhaps the best example of this, since it contains no tung oil and never has. Other choice ones include "feed and wax" (wood doesn't need 'feeding'), "Danish oil" (not made from Danish people) and "teak oil" (not made from teak and not specifically intended for finishing only teak).