I bought this a year ago and planted it in partial sun, putting mulch over the top. It had about a dozen flowers on it, and faired well during our midwest winter. So far this Spring, only 3 flowers are showing. Will more appear?

It might be mulched too deeply or planted too deeply (it has surface roots). It might have been overwatered (one thing that truely upsets it). It also might have gotten too cold in the winter and some of the buds froze. It is hardy from zones 5a to 9b, so if you are on the "fringe" of those ranges or beyond them, expect some reduction in size and performance or if you soil is deeply acidic or highly alkaline - it tolerates a good range of acidity levels, but some areas do tend to naturally fall outside the acceptable range - in which case supplements could help.
You also could potentially have too much nitrogen going on there - which would produce lots of leaves, but fewer flowers, in which case a more balanced fertlizer - or less fertilizer - would do the trick.

consider that your snowball viburnum was 'forced' into bloom at the greenhouse so it would look good to you so you'd buy it.... now, it needs time to develop a good root system and make new branches.... this will take time.... the third year is usually a good one... and ever after....