I have read in a book called Medicines of the Prophets that it says that we should be Physically active. It said preferred activities are horseback riding, archery, wrestling and running.
What is your opinion on these on whether they are Halal activities or not and whether I should really do it or not?
The physical activities described in your question are not only Halal (permissible) but they maybe considered Sunnah activities because the Prophet Sallallahu Alaihe Wa Sallam either encouraged Muslims to perform these physical activities or performed them by himself during his blessed life.
There are multiple Ahadith of the Holy Prophet Sallallahu Alaihe Wa Sallam that encourage Muslims to engage in physical activities such as swimming, running, wrestling, archery etc...
A Muslim should do his best to keep himself fit physically. The Holy Prophet Sallallahu Alaihe Wa Sallam also said" A strong Muslim is better than a weak Muslim".
The list of allowed physical activities for a Muslim is not confined in the above. Any physical activity would be permissible as long as it does not violate some principle of Shariah or causes the wastage of time.
And Allah knows best.
Mufti Ikram ul Haq
Fatwa Center of America