Legality/advisability of sheltering currently liquid assets into a mortgage?

Initially posted in /personalfinance but was removed as the situation is largely legal in nature.

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Background: I currently work a job making roughly 32K a year and have a mortgage on my home. Due to diligent saving I currently have about 30K in liquid (non-retirement fund) assets.

Situation: I am planning to try and go back to school to finish a degree needed for a possible career advancement and also have a potentially large medical expense looming. As such I am looking into both Financial Aid for college and Charity Care programs for the medical expenses. Based on my income I should be able to qualify for both but I am concerned that having those assets available may hurt my eligibility.

My question: Is it A: legal and B: advisable to spend down a large portion of my assets on reducing my mortgage principal in order for those liquid assets to not be considered when determining my eligibility for aid.