No, that doesn't work. Don't worry about attributes on that matter, but you need to know which adjectives belong to which noun. Both kicsi and szőrös define állat here, and they are in front of it, so they won't change when állat changes. "Kicsi, szőrös állat" forms a unit, and only the last word in a unit receives any suffixes or something.
The other possibility would be without an additional noun: "Az egerek kicsik és szőrösek" - "Mice are small and furry." Also note it's szőrösek, with -ek. Adjectives usually get -ak/-ek suffixes.
Woaw ! Theses are great, clear and very helpful explanations !
(BTW : "great, clear and very helpful" are in front of "explanations" and make a group, so they wouldn't take the plural in hungarian. But if I had "Theses explanations are great, clear and very helpful", then they would take the plural since they become attributes)
Nagyon köszönöm a ségítségét !