How limiting is a rigid bike?

I've been wanting to expand my cycling a bit lately to include more off road riding. I have no intention of racing or going to a trail centre or anything like that, just exploring tracks and bridleways. I think I've heard it classed as rough stuff cycling. I don't currently own a mountain bike and don't really have the money to buy a decent new one. I've been thinking about buying an old rigid mountain bike because even fairly high quality ones can be had for quite low cost. I really want to steer clear of the weight and maintenance issues associated with cheap or old suspension forks. I am also thinking that a rigid bike should be more versatile and could alternate as a cheap touring bike if fitted with racks. The question is how would the lack of suspension limit me off-road? People went mountain biking before suspension. If it is mainly a case of being slower I'm not bothered about that. Is it just a case of using wider tyres and dropping the pressure a bit?

Any help will be apprecited.

I didn't find the right solution from the Internet.

References:

https://forum.cyclinguk.org/viewtopic.php?t=82822

Thank you.