[You probably won't need all of this info but I was busy typing it while posts above were appearing! I might as well post it anyway in case someone finds it useful...]
I have been on warfarin since 2012 after DVTs and PEs in 2012 and 2013. I was taken off it after recovering from the first clots, but I developed them again the following year so I was put back on anticoagulants. I will take them for life now.
I took 8 months off the bike the first time round. I was too ill to cycle for the first 5 or 6 months, but extended the break because I was too scared to risk it!
Eventually I decided that being unfit was probably more risky than cycling so I got my bike out and started again. It took me at least 6-8 months to get reasonably fit again. I never got back to full fitness though, probably due to long-term damage to my lungs. I get by, but will never be superfit!
It took me a long time to stop worrying about what might happen in an accident. Ok, an accident to me could be more dangerous than to somebody who was not on anticoagulants, but I am pretty cautious anyway so hopefully I will avoid a bad injury. Definitely no downhill mountain biking for me!
I make sure that the people I ride with know that I am on warfarin in case I am injured and unable to tell paramedics about it. I wear a medical dog tag with the info on. It might not be spotted, but it can't hurt! I also have my medical info accessible on my phone's lockscreen, though it might be easier just to write it on a card and carry that about with you.
The warfarin itself doesn't appear to affect how I feel.
If you are on warfarin then you need regular blood tests to keep an eye on what it is doing to you (coming up with a number called INR). Too much will greatly increase the risks. Not enough and it won't be giving you enough protection.
Your INR will potentially be nobbled by what you eat. Warfarin works by influencing what happens to vitamin K in your body. You get vitamin K in certain foods, such as green vegetables. I was given terrible advice by one nurse, which was to pretty much cut vitamin K out 'because warfarin is trying to protect you from vitamin K'. That was really unhelpful. If you didn't have any vitamin K in your diet you would virtually become an haemophiliac. Consistently eat plenty of greens so your body is topped up with vitamin K and then your warfarin dose can remain stable. If you constantly change your diet the warfarin dose will end up being changed regularly and it is a nightmare! I have got it well stabilised now and have been on the same dose for years.
Another thing - there are more modern anticoagulants now. Ask whether they might be suitable for you. If so, you could avoid the need to have the frequent blood tests, and have more freedom in what you eat.
Good luck!