Is my power steering supposed to be whining?

Well every cold morning when I start my car ( it doesn't do it once it warms up ) my power steering likes to whine slightly, not too loud. The hum accelerates with my RPMs, and also while doing a 90 deg. turn. So it does have something to do with the steering, but I'm just wondering if that's normal just because it's cold... or should I get it looked at? I'm new to the Tacoma scene, and new to the power steering scene also, so I'm not sure what to be looking for... any help would be appreciated thanks.

My '03 V6 does the exact same thing. I have just 2500 miles on it. I checked the power steering fluid level and it is full so I quit worrying about it. That is why I have a warranty. If I didn't, then I would be replacing the fluid with a high quality synthetic ASAP. The logic here is that synthetic flows better at low temps. The whine is the exact same sound the pump makes when it labors hard against a rock or something off road so in reality it is just working harder than it needs to against cold fluid.

I to had a whining power steering pump.I took the power steering top off and it looked full,but after i added about 4 to 6 oz. of fluid it quit.I have seen a few articles from people with 03 toyota tacomas with leaking p.s. pumps. My 2003 Toyota Tacoma dual cab 4x4 has 20000 miles on it and i have a leak somewhere on mine.I just haven't had time to take it to toyota. I looked for the leak and it almost looks like the hose fitting is leaking where it was pressed together.I am going to let toyota worry with it.But it seems to me like 2003 toyota tacomas have power steering leakage problems