The heel of my foot hurts to walk, would soaking in hot or cold water be beneficial in any way?

Not very much...: Support is more important. Most shoes aren't always what is bad, usually it's the crummy insoles they come with! there are many possibe reasons (plantar fascitis leaps to mind) that you may have pain in the heels, but try arch supports like spenco polysorb insoles (http://www.Spenco.Com/products/footcare/poly-sorb) and otc anti-inflammatories (like aleve). If these don't help, see a podiatrist.

It might: Ice can be beneficial in reducing the heel pain, and heat can help with the symptoms of stiffness. Using an antiinflammatory, doing stretching exercises and looking at your shoe support situation (and potential need for arch support) may provide greater benefits. Talk to a podiatrist about this.

Combo treatment. : If you have plantar fasciitis, and hurt most with the first few steps in the am, the more you can do together, the better: #1: supportive shoes. #2: firm inserts/orthotics. #3: oral antiinflammatories (check with your dr). #4: stretching your foot/calf. #5: icing (10 min at a time). You may also need physical therapy or cortisone injections, or eswt if available in your area. Soaking won't help!