Should I share my horrible software?

Yes, you should.

First, most scientific software is terrible. I'd be very surprised if yours is worse than average: the mere fact you know design patterns and the difference between recursion and loops suggests it's better.

Second, it's unlikely you'll have the incentive or motivation to make it better unless, or until, it's needed by someone else (or you in 6 months). Making it open gives you that incentive.

Potential upsides: possible new collaborators, bugfixes, extensions, publications.

Potential downsides: timesink (maintaining code or fixing problems for other people), getting scooped. I'll be clear: I don't take either of these downsides very seriously.

I would clean it up a little and share it. I've released a lot of code over the years, and also not released code for the reasons you give.

Go through it and and comment it, at whatever level you can. Leave in "failed attempts" and comment them as such. Say why they failed, and what you tried. This is VERY useful info for people coming after you.

Make a README file that says you are releasing it on request in the hope it helps someone. Say that you know the code is ugly, but you hope it's useful anyway.

Far too many people hold things back because it isn't perfect!

Yes! Especially if your paper is e.g. about a new/improved algorithm that you've implemented, or you do significant non-standard data analysis, or basically anything where reproducing your results means re-implementing your software.

Papers seldom have room to give more than an outline. I know I've spent (= wasted) much too much time trying to implement algorithms from papers that left out critical (but not strictly relevant to the paper) details.