How do I sample the color from one object in an image to another object in a second image?

Yes, Linda.  Once you set the background color by any method, it will be available for a different photo.

So, here is one way to blend the face into the mountain.  I assume you already have the mountain as a background layer and the face superimposed as the second layer in the image.  I also assume that the face is in color:

• First, use the color picker tool to create a shade of grey from the mountain in your photo.  (You could actually use any shade of grey from the color picker panel.)
• Next, select the face layer in the Layers panel and create a new blank layer:

• Select the blank layer and use the Paint Bucket tool to click on the image and fill the layer with the foreground grey color.  The image will be filled with that color.
• Change the blend mode of the grey layer to Color. 

• The entire image will now be black and white.  But we only want the face to be B&W.  So, we only want the grey layer to affect the face layer.  To do this, we create what is called a clipping mask.  Now, press the Alt-key and hover the mouse cursor between the grey layer and the face layer.  When the cursor changes shape to a white box with a down-facing arrow, click the left mouse button.  The layers panel and image should look something like this:
  

•  Next, select the face layer and reduce its opacity to further blend it into the background:
  

And for a finishing blending touch:

• Select the face layer, create a layer mask and select the white box mask so it is outlined in blue:

• Press the B-key to select the Brush Tool.  In the Brush tool options, change the Opacity to a low number something like 20%:

• Now paint with the brush on the face in the image.  You can paint over the same area several times to increase the effect of the brush.

You should end up with something like this.  Hopefully, it is your desired result:

And one further option for the picture as a whole, I selected all 3 layers and merged them by pressing Ctrl+E.  I then pressed Ctrl+L to bring up the Levels control and adjusted the gamma button to darken the stone, which gave me a better blend of the face.  This is probably way more information than you wanted, but hopefully, you will find it useful.

• Select the photo that you want to be the source of the color
• Click on the foreground color patch at the bottom of the tool bar.  The Color Picker panel will open.
• Move the cursor over the color in the photo you wish to match and the cursor will change to an eye-dropper shape.
• Left-mouse click on the desired color.  That color will now be the foreground color.
• Click OK in the panel.
• Alternatively, choose the Color Picker tool or press the I key.   In this case, the Color Picker panel will not open.  However the foreground color will change to your chosen color after you click inside the source photo.

Do you need instructions for how to change the color of the face to blend into the mountain?