If the job is only open for a short period of time, then waiting until after the holiday/New Year risks that the window will have closed, and you won't get the job.
If the job is posted as a way to snare applications, then applying without knowing if the need is real is just the luck of the draw. They might just evaluate the applications submitted in the last 30 days whenever they need to find a web developer. They would assume that any older than 30 days are from people that have found jobs. (Don't get hung up on 30 days, it could be 60, 90...)
If they never update their page, then applying might be a waste of time because that job closed years ago.
See if you can contact somebody in the company via phone, email, or through LinkedIn. Do this to determine who does the hiring. It is also possible that they use an outside firm to gather resumes for some positions. The outside company does the initial screening. It is luck of the draw that this company will find you and pass it on to the small company.
Sending in an application that risks getting lost in the pile, wastes little time, but it does waste the opportunity. Focus on selling yourself to them, research them and find a way to contact them, so you know when and how to apply for the real jobs.