It all depends what you want to do, and if you want it to index (I assume so).
The age of the bike creates some challenges, as you are running 7s. 8s or 9s would make things easier, but no problems are insurmountable.
Moving to drops means changing all your controls, and possibly your stem.
Putting drops on your current stem may seem a quick/easy/cheap fix, but you have to consider that (even riding on the hoods) your hand position will be about 4 inches further forward than you were on flat bars. On older MTBs (which had shorter top tubes) this will be not so much of a problem. Try it and see ...
... with one caveat. Make sure that (if you use the original stem) that the clamping diameter of the stem is compatible with the clamp diameter of the bars. There are plenty of threads in here relating to that (and some people ignore the difference completely with success - but it is worth thinking about).
You will need to change brake levers. Older style (non STI/Ergopower) road brake levers will work fine with the short pull cantilevers that you have. I have seen plenty of instances where riders are using MTB style levers on the flat sections of the road handlebars - do whatever you want - as long as it is safe.
More recent style MTB levers (designed for V-brakes) pull more cable than the older style, and (while they will still work OK) are not really the best idea.
Shifters is where your problems are easily sorted, or not so easy (depending on what you want).
7s is the achilles heel here. It's getting on now (actually, so is 8s), so finding shifters that will mount on road bars may be hard. Bar-con shifters (fit into the end of the bars) work great, should be relatively cheap second hand, but must be 7s to index correctly. That means they will be about 10 years old, and hard to source.
As far as I am aware, there are no 7s STI/Ergo shifters available.
If you can afford it, convert to 8s (new chain, rear cassette, axle and freehub*). It's likely your chain and cassette are getting old now (if they have never been replaced), and this will greatly improve the likelihood of getting STI/Ergo shifters. Heck you could even go 9s (new chain and shifters and MAYBE new FD).
* might be easier to get your wheel rebuilt with a 9s hub (good for 8s and 9s)
8s and 9s STI will work fine with your rear derailler and well enough with your front derailler (MTB FDs and Road shifters have different pull ratios).
8s and 9s Ergo power (Campag/Sachs) will require you to match with the same manufacturer RD (and a couple of other tweaks that we can guide you through when you get to that point).
All in all, a great upgrade, and older MTBs do ride well with drops, but there are a few considerations to get it "right"#. I have done this several time before on my own and customers bikes. Let me know if I can help.
# all in the eye of the beholder/shifter