By strength, I assume you mean "Cooling Power". The rule of thumb for Swamp Coolers is "1 square foot of pad area will deliver maximum results for 125 cubic feet of room space". Of course, that is considering you have "Ideal Conditions": in which case you can expect a 20 degree (farenheit) drop in temperature. For less than ideal conditions, the temperature drop will be less!
Some things to keep in mind for achieving "Ideal Conditions":
1. A low humidity environment (the lower the better!).
2. Adequate air movement over the pad(s).
3. Adequate water distribution to the pad(s)
4. Thickness and materiel of the pad(s).
Yes, it will make the room more humid - but that is a benefit in a low humidity environment (which is the only place a Swamp Cooler can really work to it's potential).
Blowing hot air over ice is just going to keep you busy replacing the ice. I have serious doubts that it would do much good (others may disagree). I think it is one of those "Sounds good, Feel good" kind of solutions. In less, of course, you are talking about massive quantities of ice, but that creates it's own problems!
