The real issue is in the word 'disaster'. The thing that makes almost all 'natural disasters' into 'disasters' is the fact that the humans who suffer are ill prepared for the event. In many (though not all) cases the disaster can be prevented if we prepare better.
For example, good building standards significantly reduces the damage due to earth quakes. Hurricane Katrina flooded New Orleans because they hadn't built the levees high enough.
So, is God responsible for helping us prepare? Is nature?
Every time you hear about a natural disaster, listen carefully and you will hear something like this:
"This was the worst ..... in the last ..... years."
That means it has happened before!
In many parts of the world, there are seasonal changes that we know about and adapt to. Even many animal species migrate because if they didn't it would be a 'natural disaster'.
If people didn't turn on their central heating in the UK in winter, it would be a 'natural disaster' every year. Should we blame God or nature for the winter cold?
Our problem is that we cant seem to plan well more than a few years ahead. It is partly due to most political systems being built around a relatively short cycle, and partly simply humans habit of only making short term plans.
In our defense, we do sometimes get it right, and most places do have building codes to cater for earthquakes, flood walls to protect against floods etc and most disasters become disasters because those plans that were put in place were not followed.
I am not so much trying to defend God or nature but rather pointing out that we should stop trying to absolve ourselves from the blame. We shouldn't just send money to Haiti, we should as ourselves which other parts of the world are subject to earthquakes and do not have buildings up to scratch and try some preventative medicine for a change.
The difficult questions regarding God is, if you jump off a cliff, can God prevent you from hitting the rocks below, will he and should he? And if you fall off the cliff due to stupidity, carelessness or mere freak accident, can God prevent you from hitting the rocks below, will he and should he?