I wouldn't change out the contactor unless just for the heck of it. Especially if the noise stops when you turn off the breaker for the outdoor system (while leaving the air handler breaker on) with the heat "on".
In the past three days, working in the Huntsville area we have took or ran 5-10 calls a day with ice building up on fan blades from the misty rain or water dripping off of roofs, that'll definately cause some noise issues and make a fan run out of balance. If you see no ice on the fan blade and everything seems to be running smooth it's probably just due to the fact that it's past its structural balance point and running at the max that it can. When the weather pushes units to their max it's not uncommon for them to make a little more noise, especially on builder grade equipment. Also as several others stated, lack of routine maintenance can also make things a little worst in the peak seasons.
I'm a service tech at a large reputable company in Huntsville. If you need someone to come out and look at it, shoot me a pm with a ph number and I can get you some info.

Just some observations:
*Listening to the noise on the link, it sounds very much like a bad bearing or something hitting the fan blade.
**It also kinda sounds like a chattering contactor.
***The breaker the OP said was turned off was labeled "heat". This tells me that he turned off the AHU inside which has the LV Xformer which in turn would shut down the outside unit also.
****the better test would be as Steelman noted, turn off the disconnect to the outside unit while leaving the inside AHU running. This disconnect should be located next to the outside unit. This way the contactor will stay engaged while the unit stops due to lack of power. If the noise remains, it's the contactor. if it stops it's something with the units moving parts, ie; fan, compressor or combination.

Okay, this time, I killed the outside unit at the outside disconnect and took a video while heat was ON at the thermostat. Is that a normal sound? Its a little louder in the video. You can download the new video here: SOUND

Is that the noise that you have been hearing that is concerning to you when the system is running? From what I can tell from this video the noise sounds as if its a contactor buzzing. If the noise I hear is the same noise that you recorded, if that makes sense.

Yall having to enter credit card info to listen to this video? It won't let me just listen to it with out signing up.

It pulls up another web page for me then has a download link.

Steelman hit it....it's the Contactor. An easy change out.

With the power to the outside unit off and the inside unit on, the contactor is the only thing outside that will have power to it being that it is low voltage controlled and low voltage comes from the xformer located and powered in the inside unit(AHU)

Don't nobody want to listen to squirrelman

Okay, so you guys think its worth changing out the contactor. Anything special that I need to know?

If you believe that the noise you hear is from the contactor buzzing, replace it. They are inexpensive.

You'll need to know if you need a 1 pole or a 2 pole contactor. They are simple to change out, just kill the breaker at the outdoor unit and the breaker for the air handler. Replace the part 1 wire at a time or label them.

Okay, I changed the contactor and the noise is still there. I've looked at a few videos online and the closest thing Ive found that describes the noise is that it sounds like its constantly running in defrost mode...but with the fan on. Again, when the unit turns off, theres no noise at all. Does that make sense? Any other ideas? Thanks!

I didn't think the contactor would help much.. I would just call a company to come look at it. A diagnostic fee should be around 50-60 bucks and then you'll have a definite answer.

Wait.....didn't you say that you turned the outside unit off when you recorded the 2nd recording? Was that noise coming from the outside unit with the disconnect to it turned off and ONLY the inside unit running?

With the outside unit off the only thing that can be powered will be the circuit board and the contactor. They are the only things that are Low Voltage powered and that Low Voltage power comes from the Transformer inside the inside unit.
With the outside unit off the compressor won't be pushing refrigerant thru the lines so there shouldn't be much noise coming from that.

I agree with jbatey, call a professional to come out and look at it.

probably heat pump and the noise is normal

Well, in case anyone is interested, the HVAC guy just left. Looks like my compressor is going bad. Says it is working, but not well at all. Good news is the part is under warranty...bad news is the labor, etc...isn't. I need to learn to replace compressors! Heh...well, at least I know now!