Your animal does not change; what changes is the year around it. 2034 carries the number 9 (from 2 + 0 + 3 + 4), which sets the tone the Horse is operating inside.
Those born in the Year of the Horse are energetic, free-spirited and sociable. This makes them reliable company, natural problem-solvers and people others instinctively trust.
What follows from pairing an animal with a year is an emphasis: some habits get rewarded this year and others get expensive.
More on the Horse: Horse zodiac · Horse in 2026 · the number 9 · zodiac signs · tarot readings · numerology
Years are not good or bad in the Chinese system — the annual cycle emphasises certain things and de-emphasises others. Whether that reads well depends on what you are trying to do.
No. Your animal is fixed at birth by your lunar birth year. The year animal is the cycle around you.
On Chinese New Year, which falls in late January or February — not on 1 January. Check the exact date for that year.