I was watching a movie with a "medieval" setting and it occurred to me that whenever you see them in a small village or hamlet they're always working and there's no way that with such a small customer pool, even taking into consideration people coming in from smaller surrounding settlements for fairs and emergency services, could keep them busy/ in business the whole year round. Even using slow times of the year to back-stock common items (nails, hinges, etc) you'd eventually run out of things to do.
Follow-up question: How did Medieval rulers succeed in ramping up production for war? If the peace-time economy wouldn't support the full blacksmith occupation (as the original question posits), how do they get the weaponry they need in short time?
For that matter, was obtaining the metal ore needed for weapons as simple as sending extra serfs into the existing mines or buying it on a market?
This is something of a hard question to answer, as the lives of the common people are very poorly documented in general. However, I'll try to answer this to the best of my ability. Some of the best sources are, unfortunately, quite obscure and out of print, so I'm relying mostly on works that cite them.
Small villages did sometimes have smiths. Cuxham, in south Oxfordshire, was a village with somewhere between 125 and 150 people in 1298 and had its own smith. Some villages, such as Wharram Percy, were twice as large and others were even upwards of five hundred people, while others were much smaller, with only a few score people. Cuxham is quite a good example, then, of what a smallish village with a smith would be like.
Regarding how many days a year a smith might work, this has a lot more to do with the religiously mandated holidays. Straight off the bat, fifty two days a year (Sundays) are meant to be work free. Added to this were the four major Marian festivals (Mary's Divine Motherhood, her Immaculate Conception, her Assumption and the Annunciation of the Lord), the days sacred to the apostles and evangelists, Christmas week, (theoretically) the two weeks of Easter, and any local saint's days. As a result of the last part, the total time taken off work varied from place to place, but was probably between 80 and 100 days per year. Don't forget, however, that the usual work hours were daylight hours, so potentially seventeen hours or so during the height of summer. The average work week was about 56 hours, with winter and summer hours evened out.
Now, how many days per week would a smith work at their smithy? That's much harder to assess. The demesne alone had six horses and, while my sources don't specify how many horses the villagers owned, other early 14th century villages usually had an average of somewhere between 1.5 and 2 horses per householder. Horses were relatively cheap compared to oxen at this point, and could plough most fields faster than oxen (although oxen were better for very heavy clay or rocky soils), and they very rapidly replaced oxen at the end of the thirteenth/the start of the fourteenth century. The dominance of the three field system and the resulting surplus of oats in most part of England likely enabled the proliferation of low quality horses among the poorer English peasantry at this time.
If we take the total number of horses as 50, assuming a low number among the peasants, that's 50-100 shoes per year and 1200 nails. The Cuxham smith mostly sold each new horseshoe with 12 nails per shoe, which has been taken to indicate that the shoe would last long enough for reuse (six nails per shoe was typical of the period). Based on 19th century practices, each horse was probably reshod every 3 months on average and, considering the extra nails, shoes would have lasted at least six months. In exceptional cases, the shoes might have lasted a full year. The archaeology certainly shows that shoes were frequently worn until they were completely unusable, at any rate. How long it would take to reshoe each horse is impossible to know. It depends so much on the skill of the farrier (the smith in this case) and the temperament of the horse, and the extended period of time a horse went without being reshod compared to modern practice (3 months vs 4-6 weeks) makes modern estimates hard to apply. A conservative estimate might be one hour per horse, or 200 hours per year, plus 70 hours for making the nails. I can't find any information on how long a horseshoe takes to forge, unfortunately.
This clearly isn't enough work for a smith. There are plenty of other jobs for them, however. Making knives, repairing the metal components of mills and carts, making or repairing scythes, etc. The Cuxham smith would also have been servicing more than just his village. Some other villages of Cuxham's size wouldn't have had a smith, having a carpenter, thatcher or other skilled worked instead, and if Cuxham was close enough then its smith would have serviced them. The smaller communities around Cuxham would also look to its smith for their own needs.
With that said, there still wasn't enough work for the Cuxham smith to work at his forge full time and he did have land of his own. I haven't been able to find out the exact size, but based on practice going back into Carolingian times it wouldn't have been enough to live off, but would go a long way to supplementing their income and give them something productive to do with their off time. This was a typical practice for most medieval tradesmen in villages and small towns (which were almost always semi-agricultural in nature). During harvest time, where labour was at a premium and every hand was needed, they might even have spent more time working in the fields than sharpening or repairing tools.
I hope that's gone some way to answering the question for you!
Bibliography