"The famous kindergarten teacher is arriving on a white horse."
Translation:A híres óvónő fehér lovon érkezik.
The words that acquire this 'v' are generally very old words in the language and may have some other quirks. In addition to the ones which Shamarth mentioned, here are a few more (with some examples of forms in which the v appears; not every form makes sense with every word):
hó (snow): havat, havazás, ....
fű (grass): füvek, füvet,
cső (pipe): csövek, csövet, ...
lé (juice, liquid, or broth): levet, leves (which can be an adjective, or the noun meaning "soup")
szó (word): szavak, szavam... (gets 'v' in plural forms but mostly not in singular)
mű (work, creation, opus): művet, művek, művem, műveim (unusually, doesn't shorten the ű).
In some cases you can see a rare remnant of the connection with Finnish: for example, Hungarian "kő" (stone), when it acquires its 'v', shows its relation with Finnish "kivi."
This happens to some one-syllable nouns that end in a long vowel. Whenever a suffix that starts with a vowel or requires a link vowel is added to them, the vowel of the stem becomes short, and a "v" appears.
Ló + (o)n - lovon; ló + (a)t - lovat; ló + (a)k - lovak
Kő + (ö)n - kövön; kő + (e)t - követ; kő + (e)k - kövek
Tó + (o)n - tavon; tó + (a)t - tavat; tó + (a)k - tavak
It doesn't happen when these words are followed by suffixes that start with a consonant: lóval, kőtől, tóról.
Of course there are exceptions: "lóig", "tóig", "kőig"; "dó" (do, used in solmization) - dók, etc.
I didn't find any resources to this topic, so any additional information and corrections are welcome.