The text on the sign consists of two sentences and a signature. Sentence 1 says:
This path will not be cleaned when there is snow and will not be gritted on black ice.
This is an information about the habits of the owners of this path. Knowing this fact is without any consequences for the reader. It is just a neutral information.
Sentence 2 itself also consists of more than one part:
Die Benützung ist verboten.
Use is prohibited.
This is clear: You are not allowed to use this path.
But there also is the word deshalb which means therefore or for this reason:
Die Benützung ist deshalb verboten.
Therefore use is prohibited.
This word just informs you about the reason why this prohibition exists. It does not transform the prohibition itself. This reason is what is said in sentence 1, but in fact it doesn't really matter why it is forbidden to use this path. It still is forbidden. It is forbidden without any exceptions, i.e. for everybody, at any time and under all circumstances, including warm summer weather.
The second part of sentence 2 says:
Use at your own risk.
This means: You can't blame anybody else but yourself if something bad happens to you when you use this path. For example: When you walk there on a warm summer day and from a rotten tree breaks down a branch while you pass under it, hits you and breaks your arm, then it's your fault.
But this second part is superfluous, because using this path is forbidden anyway. It is like if you break in a house to steal something. This also is forbidden. If you stumble over a carpet you didn't see and break your leg you also can't blame the owner of the house.
All in all this sign contains lots of nonsense. But still the intention is clear: If you use this path when there is snow or black ice, you do it at your own risk.
This is a better text:
Dieser Weg wird im Winter nicht geräumt und nicht bestreut. Bei Schneelage und Glatteis erfolgt die Benützung daher auf eigene Gefahr.
This path will not be cleaned or gritted in the winter. Therefore when there is snow or black ice use is at your own risk.