Weak Analogy?

I wouldn't say a weak analogy, but it would be a non sequitur , an argument from ignorance , and the argument is begging the question more than once.

First, I don't see any analogy being proposed here. The human body is not being compared to a snowman; rather, two examples are being presented—something nature can do and something it can't do.

Second, this argument equally proves god doesn't exist (by the same flawed logic, which we will get to):

1. Human body is more complex than a snowman.
2. God can't create snowman which is less complex than humans 
3. Therefore God can't create human and hence god doesn't exists. 

Now for the problems:

1) The fact that nature doesn't isn't the same as nature can't. The argument is begging the question by assuming impossibility. We can only assert that, to the best of our knowledge, nature has not created a snowman (charitably saying a "snowman" has a corncob pipe and button note and two eyes made out of coal, not just three rounded clumps of snow on top of each other)—not that it is impossible for nature to create a snowman. This would allow us to reject premise #2.

2) The argument is begging the question  by assuming complexity is the reason for nature not creating the snowman. This would be like saying because I can't lift a one pound rock on the moon, I can't lift a two pound rock here on earth. I can't lift the one pound rock on the moon because I can't get to the moon. Nature wouldn't create a snowman because the design is not consistent with natural selection—it is just something nature wouldn't do based on everything we know about nature.

3) Based on #1 and #2, the first part of the conclusion is a non sequitur — it doesn't follow.

4) The "hence god exists" is a simple argument from ignorance or more specifically the God of the gaps. If we did manage to rule out nature, it would be something else (perhaps aliens).