My English teacher at school was adamant that on to was always two words, a position which is acknowledged by ODO:
The preposition onto written as one word (instead of on to) is recorded from the early 18th century and has been widely used ever since, but is still not wholly accepted as part of standard British English (unlike into, for example). Many style guides still advise writing it as two words, and that is the practice followed in this dictionary. However, onto is more or less the standard form in US English and in the specialized mathematics sense. Nevertheless, it is important to maintain a distinction between the preposition onto or on to and the use of the adverb on followed by the preposition to: she climbed on to (or onto) the roof but let’s go on to (not onto) the next point.
In British English, it’s always safe to separate on to; in American English, onto would appear to be acceptable in almost all circumstances.
If onto can be one word in the examples given, one has to decide whether on can be classed as an adverb with to as the preposition, or whether onto is an acceptable preposition in its own right.
In Burchfield’s New Fowler’s Modern English Usage he quotes Fowler from 1926:
Fowler (1926) added ... examples of on used as a full adverb before to and therefore written separately: We must walk on to Keswick; Each passed it on to his neighbour; Struggling on to victory. In He played the ball on to his wicket, he judged that “as He played on could stand by itself, it is hard to deny on its independent status”. It should also be noted that They drove on to the beach would normally mean “They continued their journey until they reached the beach” but could also mean ”They drove their vehicle to a position on the beach”; whereas They drove onto the beach could only mean ”They drove their vehicle to a position on the beach”.
With hold on, the on has Fowler’s “independent status”, and there is no sense of movement as there is with driving “onto a beach”. Indeed, the act of holding on to something is precisely to steady oneself and prevent movement! Hold on to is therefore appropriate.
In the second example [“grabbed onto the cushion”], with the verb grab on the to is needed (so on is not independent), and there may even be a sense of movement with a sudden taking-hold of the cushion. Grab onto might therefore be appropriate.
That said, customary forms in different dialects of English may dictate a different use. Grab onto looks decidedly wrong to my British eyes, conditioned as they are, even though I’ve argued fairly successfully from Fowler [a respected British authority] that it’s reasonable; and hold on to may look decidedly wrong to American eyes.