I have been terrified of snakes my entire life. If I saw one at my house, I'd be outta here. We have some acreage and I used to ride the tractor to mow. If I saw a garter snake, I was done... finished.... the end. And I was sitting high on an old, old tractor.
I used to not be afraid of heights, but as I've aged I've developed that "quirk", too. And that is getting worse the older I get. I can't even walk in a building higher than the 3rd floor any more. I break out in a cold sweat and freeze - I can not move.
Regarding nature hikes -- it will depend on what your wife feels comfortable with. It's not a situation that we have any control over. We go down by the river from time to time, just to sit and watch the boats out on the water. I am not terribly comfortable, as I am constantly scanning the ground for snakes.
If one is terrified of something to that extent, pushing them isn't the answer. No one will have any fun.