Arbitrariness and coinages

This is a good question because it reveals the problematic nature of the arbitrariness axiom in modern linguistics.

The relationship between sound and meaning is indeed arbitrary when you look across languages. What is dog in English is hund in German. What is 'pig' in English is 'Schwein' in German. There is no inherent relationship between them. When you put them together you get 'pigdog' and 'Schweinhund', and because the relationship between sound and meaning is arbitrary, you get a pig hunting dog in English and an insult in German. (Although calling someone a 'pigdog' in English is also insulting, it's not a very common one.) But even in the case of perfect calques, e.g. Czech časopis [magazine] is formed exactly to follow the form of the German Zeitschrift (lit. time-writing), the relationship between the sound and meaning is arbitrary cross-linguistically or even intralinguistically. The sound for magazine in both languages could have been totally different. This holds even for onomatopoeic words which are motivated by the referent but still fairly arbitrary across languages (e.g. compare the word for cock crowing across languages).

However, while this principle is obviously (axiomatically) correct, it is not very informative. Even Saussure (who first proposed it) noted that native speakers often associate the sounds with meanings as if they were natural. This was later confirmed by various research in phonosemantics. The logical arbitrariness co-exists with universal tendencies in sound meaning as well as language-internal processes of aesthetic associations between sounds and meanings. This is much more interesting and useful to study than the relatively uninformative arbitrariness axiom. Of course, it is important to remember that it was established in a context of theories proposing essentialist connections between sound and meaning which are easily disproven by the data.

The sort of thing you're describing is not usually a case of sound symbolism but simply the semantics of compounding which will always be somewhat motivated (although in many cases, the original meanings will be opaque to most speakers).