Prepositions – ‘Agree On’ vs ‘Agree With’ vs ‘Agree To’

The meanings are very similar, and these three prepositions can be used almost interchangeably, particularly in the context of your "The mountain is covered with/in/by snow" example. But some subtle nuances may apply.

When referring to a substance that sticks to another, use in or with, but not by:

• The actress was covered in blood, or
• The actress was covered with blood, but not
• The actress was covered by blood.

Another example:

• The ribs were covered with sauce, or
• The ribs were covered in sauce, but not
• The ribs were covered by sauce.

When referring something that physically protects something else, use with or by, but not in:

• The field was covered with a tarp, or
• The field was covered by a tarp, but not
• The field was covered in a tarp.

Use covered with to indicate an unusual amount of something on top of something else; use covered by to connote a covering so dense that the object being covered is completely obscured from view:

• The mountain was covered with fog.
• The mountain was covered by fog.

Another example:

• Our grass was covered with butterflies.
• Our grass was covered by butterflies.

Somehow, the latter (covered by) paints a picture where the butterflies are so close together that I can hardly any the grass at all, but in the former (covered with), I picture a lot of butterflies, just not necessarily so many that I can't see the grass.

When talking about metaphorical coverage, use covered by:

• The roof damage was covered by insurance, but not
• The roof damage was covered with insurance, or
• The roof damage was covered in insurance.

Another example:

• The city council meeting was covered by the news station, but not
• The city council meeting was covered with the news station, or
• The city council meeting was covered in the news station.

Other guidelines are likely to apply as well. This is not a question with an easy and straightforward answer.

"I cannot agree with you more." means that I agree with you to a complete extent, making it impossible for me to agree with you to a greater extent.

"I cannot agree with you any more." means that I can no longer agree with you. I agreed with you before, but that has come to an end.

"Anymore" is a somewhat controversial word which is equivalent to "any more", but does not substitute for "any more" in all uses: you would never write "I don't need anymore supplies".

See for instance: http://alt-usage-english.org/anymore.html