As someone who has recently (as in the past 2-3 seasons) learned both skiing and boarding I can tell you that for me skiing had a bit steeper of a learning curve than boarding. Easy to start sliding around on them, but much more difficult to 'master' per-say. Having said that, the advantage you have over a complete novice is that you are more or less familiar with the sensation of engaging edges and sliding around on snow. If you can afford to buy a nice ski set-up it really opens the doors to enjoying the mountains in different ways. For my part I've discovered that I prefer powder days on the board, just because of the extra large surface you have, but making powder turns on skis is no less enjoyable. I prefer my skis on steeper terrain, the groomers, or ice conditions for the extra control 4 edges provides and the enjoyment from cruising groomers at high speeds or making quick/sharp turns.
To get back to your original question, give it a shot! Find a decent instructor and let them know you have been snowboarding for a while and would like to try skiing. My advice is to rent equipment until you are at least making parellel turns, and then decide if it's something you want to invest in. Ski boots are so important in terms of your performance, and are very much a get what you pay for kind of purchase, so the initial buy-in can be particularly expensive. Better to make that investment after you've decided whether or not you want to become a proficient skier.