Yes it is true that living a frugal lifestyle and carefully saving will generally work against you in terms of qualifying for financial aid. Of course there are many other variables in place, such as income levels when applying, but all other things being equal, a family that has saved will get less (or nothing) while a family that blew all their money on cars, expensive vacations, newest iWhatevers, and expensive coffee every day with no savings to show for it all could rake it in with financial aid. I used to work as a financial aid counselor at a major U.S. university and I saw this play out many times. It really does seem a travesty in terms of public policy, but what can we do. The same things happen all the time with loan bailouts, welfare cheats, etc.
Anyway, it still doesn't make me change my approach on saving for retirement or for children's college educations. If you intentionally saved nothing in an attempt to qualify for aid, you would be much worse off in life. It would be akin, I think, to purposely being unemployed to qualify for unemployment insurance and food stamps. The tradeoff is not worth it by a long shot. You will be far better positioned by saving everything you can and becoming rich. And even if you do qualify for financial "aid", keep in mind that many times this just means qualifying for loans, not necessarily grants. As far as government assistance goes, there is pretty much no such thing as a 100%-grant package. It will always include substantial loans, although a private college MIGHT make up the difference in grants or merit scholarships in extreme hardship cases.
I just think of paying for kids' college as an added amount I want to have enough saved up for.
One thing that can work substantially in our favor is if you can time your early retirement to coincide with kids applying for financial aid, then your income will drop dramatically (or to 0) and far outweigh the savings part in the financial need determination. Meaning, you could stand to do very well in the need determination if your earned income is next to nothing, even with some savings or home equity.
Also, qualified retirement plans are generally exempted from the need determination calculations (i.e., you are not expected to cash out your 401ks, IRA's, pensions, or other qualified retirement plans to fund college costs). So if you have a bunch saved up in your 401k/etc, it won't show up in the calculation.
If you are on decent terms with your ex-husband, I think it is definitely a worthwhile conversation to have with him about starting a college savings plan for your kids. You could agree to set up a 529 for them that he could contribute towards each year.
Good luck!