Frozen Heart costs 2775g, and provides 1500g worth of armor and 1000g worth of mana. So it would be semi-cost effective on Ryze.
However, as mentioned Thornmail is EXTREMELY powerful vs AD champs such that it should have been your choice.
Basically you paid 775g for +500 mana, and minus the thornmail effect. Thornmail effect is worth a lot more than the 500 mana, and cheaper too.
You likely already had plenty of health, by getting Odins. A Rod of Ages makes a decent 5th item also, providing a good chunk of mana, high health boost, and some less than useful AP. Will of Ancients is a competing item for that slot if you aren't getting bursted down... it gives you the spell vamp to effectively increase your health.